Wage Subsidies and the Market for Butchers - Assignment Example

Introduction to Microeconomics work Lecturer: Part One Exercise Quantity Quota If QD=1000-2p and QS=100+P, the equilibrium price and quantity may be obtained by equating the two equations as shown below. 1000-2P=100+P 1000-100=P+2P 900=3P P=300 By replacing the value of P either supply or demand equation the value of equilibrium quantity can be obtained as follows; QS=100+P QS=100+300, QS=400 Therefore, equilibrium quantity will be 400 while equilibrium price will be 300 Graphical presentation of effects of 300units quotas set by the government Price Supply 400 Demand curve 300 0 300unit Qty If 300units quotas are set by the government the equilibrium price will change as shown below QS=100+P 300=100+P P=400, this show that equilibrium price will increase from 300 to 400 which translate to 100 increase in equilibrium price. On the other hand, equilibrium quantity will increased from 400 to 500.Hence discouraging imports and promoting exports of local goods and services in order to protect local industries from foreign competition as well as encourage its growth. Exercise 2.First-Time Homebuyers Credit a) Price S1 Subsidies (A) $8000 S2 Pn=$174,000 Po=$167,000 Demand As a result of subsidy, the seller would receive a total of Pn +A=174,000+$8000 =$182,000.While on the other hand the buyers would pay a price of $166000 obtained by subtracting subsidies. $174,000-$8000=$166000 b) Computation of own price elasticity of demand and supply. Own Price elasticity of demand Percentage change in price = $174,000-$166,000×100= $800,000 = 5.6% 174,000 $174,000 Percentage change in quantity demanded= 4% Own price elasticity of demand = 5.6%÷ 4%= +1.4 Own price elasticity of supply Percentage change in quantity = 5.6% Percentage change in price = $182,000-$174,000×100=4.6% 100 Own price elasticity of supply= 4.6%÷ 5.6%=+0.82 This indicates that own price elasticity of demand indicate that for every 1% increase in price there is a +1.4 increase in quantity demanded. On the other hand, if there is 1% increase in price there is +0.82% increase in quantity. c) The seller gain more than the buyer by a difference of $182,000-$166,000=$16000 Exercise 3: Wine production a) When the companies decide to employ more inputs to produce quality wines, the amount of low quality wines produced decreases as resources are shifted towards producing high quality wines. Therefore, cost reduction may be affected in the sense that if the company decides to produce more quality wines cost will increase because of higher cost of inputs required producing quality wines. On the contrary, if the company decides to produce more of low quality wines cost will fall because few inputs may be employed. b) Application of technology will lead to reduction of time and human labor required in the production of wines. Additionally, the cost of production may reduce due to increase efficiency as a result of new technology. Therefore, the demand of other input will fall significantly. Part Two Exercise 1: perfect competition 1.1 Perfect competition 1.2 Wage Subsidies a) If MM: qm=L 0.6 K 0.4 and KK:qk=L0.5 K 0.5, wages (w)=$5 and capital(r)=$10 L 0.6 K 0.4 = L0.5 K 0.5 w r L 0.6 K 0.4 = L0.5 K 0.5 w r L 0.6 K 0.4 = L0.5 K 0.5 W r (L3/5 K2/5) r= (L½K½) w 10 L3/5× 10 K2/5=5 L½ ×5K½ 5 5 5 5 5 L3/5× 5K2/5 = L½ ×K½ 5L3/5 ×5K2/5= K½ L½ L½ 4(3/5-½) ×5K2/5 = K½ L½ 41/10×5K2/5 = K½ L½ 20K½ = K½ L½ K = 20 K½ L½ K= 20K L While L=20 and K=1 b) The long-run expansion curve in terms of labor and capital may be given as follows TC= rK+WL whereby the expansion curve may be expressed in terms of MPL=MPK w r The values of k and L may be obtained by inserting them into the long run production curve as shown below. Q (K, L) = Q ((g) (L, L)). Therefore, TC=rg[f (Q)] + wf (Q) c) The average and marginal cost for the two firms may be determined as follows; Average long run cost (LAC) =LTC= rg[f (Q)] + wf (Q)=10(20)+5(1)= $205 Q Q Marginal Cost = First derivative of the Total Cost=change in long run total cost = r+g=$15 Quantity (Q) d) Foreign firms like KK are able to survive in a competitive industry because they enter into foreign markets prepared (Cherunilam, 2010). Those firms are able to force domestic firms out of the market by selling at a reduced price and paying employee’s higher wages unlike domestic firm (Cherunilam, 2010). e) If both firms are able to stay in the market and that KK is more efficient, then A in the equation below may be determined as follows; qK =A L0.5 K0.5 201=A10.5×10.5 A=20 f) Out put price in this market may be as follows QK=20×10.5×10.5=$1.47 g) If the demand function of meat is Q=225 – 9p. Then equilibrium price and quantity may be determined as follows; QD=225-9P P=25 QS=112.5+4.5P At equilibrium,QS=QD 112.5+4.5P=225-9P 4.5P+9P=225-112.5 13.5P=112.5 P= 8.333 Q= 225-9(8.333) Q=150 h) Elasticity of demand may be determined by finding change in quantity demanded divided by change in price as shown below. 150= +18 8.3333 i) if there are 10 foreign firms and 5 domestic firms each will produce as follows Foreign:qm=L 0.6 K 0.4 = 10 =A (200.6 10.4) Foreign firm will produce (A) 1.6units Domestic:qk=L0.5 K 0.5= 5=A(200.5 1 0.5)=1.1 Domestic firm will produce (A)=1.1units j) qM = L0.6 K0.4 and qM=(200.6 10.4)=6.034 The labor input for firm MM=6 qK =A L0.5 K0.5 qK=(200.5 1 0.5)=4.5 The labor inputs for firm KK=4.5 1.2 Wage Subsidies k) The expansion path for the two firms where long run cost Average AC =LTC= rg[f (Q)] + wf (Q)=10(4)+5(1)= $45 Q Q MC = First derivative of the Total Cost=change in long run total cost = r+g=$15 Quantity (Q) l) Capital Marginal Rate of Technical Substitution (MRTS) slope Labor After Subsidies Production become cheaper Capital Higher MRTS M Cheap labor N Expansion Path Capital Isocosts (Down ward sloping) B C isoquant (Convex shape) A Labor Comments: After government provided subsidies, it become cheaper to produce as shown above in the second diagram, movement along the expansion curve towards the light leads to an increase in amount of labor employed (Carbaugh, 2011). Producer who lies on the Higher the isoquant is able to maximize production subject to his isocost (Carbaugh, 2011). m) The new equilibrium price and quantity will be at equilibrium,QS=QD IF effective wage rate is $4 P=45-4 P=$41 QS=112.5+4.5P QS=112.5+4.5(41) QS=297 Equilibrium price will be 41 while quantity will be 297 n) qK =A L0.5 K0.5 qK= (200.5 1 0.5) =4.5 o) The capital labor inputs for the two firms will be as follows qm=41 0.6 1 0.4=9 qK= (200.5 41 0.5) =29 p) Consumer surplus occurs when consumers pay less, in this case consumer surplus will be $41-4=$37, while producers surplus will the difference between expected production cost and the subsidies 45-4=$41 q) Government expenditure in this case will be the subsidies given which are $4 derived by subtracting wage rates and subsidies $5-1=$4 r) The welfare effect of subsidy provides producer with an opportunity to produce at a lower cost making the goods released into the market to be cheaper and affordable to ordinally people such as low income earners. 1.3 Wage subsidies & the market for butchers s) ) The labor demand curve may be derived as follows L 0.6 K 0.4 = L0.5 K 0.5 W r By inserting the values of w and are from the equation it can be obtained as follows 10 L3/5× 10 K2/5=5 L½ ×5K½ 5 5 5 5 5 L3/5× 5K2/5 = L½ ×K½ 5L3/5 ×5K2/5= K½ L½ L½ 4(3/5-½) ×5K2/5 = K½ L½ 41/10×5K2/5 = K½ L½ 20K½ = K½ L½ L½ =20 L= 20 =4.4721 t) Demand curve are downward sloping to the light because the higher the more it become elastic. Price elasticity of demand is given as percentage change in quantity divided by percentage change in price = 5-4.4721=+0.1056 5 = 10-4.4721=+0.5528 10 u) qK =A L0.5 K0.5 10=5 L0.5 L= 2 L=1.4142 V) Perfectly inelastic supply in market wage rate for Butchers Fig.1 Price Perfect inelastic supply D2 D1 Qty Perfectly elastic supply in market wage rate for Butchers Fig.2 Price Perfectly elastic supply D2 D1 Qty Labor supply is upward slopping in the market wage rate for Butchers Fig.3 Price Upward Slopping supply curve P2 P1 D2 D1 Qty Q1 Q2 This figure 3 represent the assumption in part 1.2, whereby, government subsidies will make production cost to fall and this will in turn leads to an increase in supply from Q1 to Q2. Exercise 2: Oligopoly 2.1Collusion a) The market price, the market output and the output of each firm and cartels total profits will be as follows; Q =225-9P P=225÷9 P=$25 Market out put will be as follows, Q =225-9P QS=112.5+4.5(25) =225units. The output will be higher because the firms enjoy economies of scale as a result of merging. 2.2 Cournot equilibrium b) $225 c)$112.5 2.3 Comparison: Perfect Competition vs. Collusion vs. Cournot d) Consumers surplus=$225-25=$200 Producers surplus=$225-10=$2215 2.4 Bertrand Competition with identical products e) Bertrand equilibrium price will be as follows if wage rates are $5 and capital rental rates are $10 The equilibrium price will be P= 8.333, this means that foreign firm (MM) will be forced out of the market because it cost of production is higher and can not than the equilibrium price. On the other hand domestic firm KK would remain in the market because it has ability to produce at a lower cost than equilibrium price. f) Bertrand equilibrium price and market equilibrium quantity given Q=225 – 9P At equilibrium QD=QS QS=112.5+4.5P 225 – 9P=112.5+4.5P 13.5p=112.5 P=8.3333 Q=150 g) The two firms out put and prices may be determined as shown below Q=225 – 9P 225=9P Price (p) =$25 Out put (Q) = 112.5+4.5P Q=112.5+4.5(25) Q=225 Units Total revenues=$25×225units = $5625 Less (-) Total cost=AC×Q=$10×225Units= ($2250) Profits = $3375 h) Given that the demand functions for the two firms are QM=145 – 6pM + 9pK and QK=100 – 9pK + 6pM Equilibrium price and quantities may be determined simultaneously as follows; QD=QS QD= QM=145 – 6pM + 9pK 145=6PM-9PK……………Equation 1 100= 9pK-6PM……………Equition2 Let 6PM= x and 9pK =y 145=X-Y 100=X-Y After adding equation two from equation one we get 45=2x-2y………………Equation 3 If x=100+y……………..Equation 4 Then by replacing equitation 4 to equitation 3 we obtained 45=2(100+y) 45=200+2y -2Y=200-45 Y=-77.5 Therefore, x=100+77.5 X=177.5 Therefore, 9pK =y 9pK=77.5 pK=8.611 While 6PM= x 6PM=177.5 PM=30 Therefore, equilibrium prices for Bertrand are 8.6111 and 30 respectively while quantities are as follows QM=145 – 6pM + 9pK and QK=100 – 9pK + 6pM QM=145 – 6×30 + 9×177.5 QM=1563 units QK=100 – 9pK + 6pM QK=100 – 8.611 + 177.5 QK=269 units Equilibrium quantities for Bertrand are 1563units and 269units respectively. It was north not worth for MM to obtain the True Hungarian product label because the company incurred low cost. The maximum amount that MM is willing to contribute is 8.611×1563units=$13459 j).KK was hurt by MMM obtaining the True label because MM paid a lower cost than KK contributed. Reference List Cherunilam, F. (2010). International business: text and cases. New Delhi, PHI Learning Private Limited. Carbaugh, R. J. (2011). International economics. Mason, OH: South-Western Cengage Learning. Read More