Explanation of the graphics figures upon budget - Assignment Example

? Question In the diagram below Linda’s budget set is depicted when she is in Adelaide. The vertical axis measures expenditure on food while the horizontal axis measures her expenditure on clothing. With her present income and given the prices of food and clothing . AB is the budget line of Linda given her present income and the prices of the two goods. Figure 1: Susan’s budget set in Adelaide The budget line implies that if Susan spent all her income on clothing she would be able to purchase OB units of it. If on the other hand, Susan spent all her income on food, she would be able to purchase OA units of food. If she allocates her income on both goods then all combinations of food and clothing she can attain are those on or within the line AB. Thus the triangle OAB defines the combinations of food and clothing attainable by Susan, given her income and the prices of food and clothing. Assuming that Susan is rational, and the law of diminishing marginal utility holds for both goods, and she has continuous and complete preferences, her preferences can be depicted by downward sloping convex indifference curves. Susan’s objective is to attain the highest possible indifference curve within the reach of her budget set. This is shown in figure 2. Figure 2: the utility maximising choice in Adelaide As shown above in figure 2, given her budget constraint, Susan’s utility maximizing choice in Adelaide is point E. She consumes OC of food and OD of clothing and this generates the level of utility denoted by the indifference curve IC1. Linda is aware that in Melbourne the prices of both goods are higher and that food is relatively more expensive than clothing compared to the situation in Adelaide. Therefore, with her present income (that she earns by working in Adelaide) Susan will be able to by lesser of both food and clothing. Additionally, because food is relatively more expensive, not only she will be able to buy less of food if she invests all her income in food compared to the amount of food she would be able to buy in Adelaide, the reduction in the amount of food she can buy will be more than the reduction in the amount of clothing she will be able to buy. What this implies is that i) her budget line will shrink inwards and ii) it will be relatively more flat compared to her budget line in Adelaide. This is depicted in figure 3. Figure 3: FG - Susan's budget line in Melbourne if her income remains equal to her Adelaide income In the diagram above, FG is Susan’s budget line in Melbourne if her income remains unchanged. Observe that not only can she buy fewer amounts of either products, the reduction in her capacity to purchase clothing had she chosen to invest all her income in clothing, depicted by the amount GB in the figure above, is less than the reduction in the amount of food she can buy if she invests all her income in food, AF. This is implied by the fact that food is relatively more expensive than clothing in Melbourne. Figure 4: Susan's new budget set relative to her old preferred bundle and utility level. Therefore, as reflected in figure 4, Susan can no longer access the utility level denoted by the indifference curve IC1 and nor can she afford the commodity bundle she preferred when she was in Adelaide. Therefore her real income will fall if she has to move to Melbourne but her income is still as it was back in Adelaide. Linda, if she has to make sure Susan accepts the offer, will have to pay her enough to ensure that her real income is at least as high as it is presently in Adelaide. There are two possible ways of achieving this. I. If Susan is paid an income so that she can purchase a commodity bundle that places her again at the utility level IC1. This implies paying her an income over her present Adelaide income that will allow her to access her old indifference curve IC1. This would be what is termed as the Hicksian compensation. The idea is that Susan will be back at her old real income level if she has access to her old utility level. Figure 5: The Hicksian Compensation - PQ denotes the budget line reflecting the level of required income This is shown in figure 5. If Susan is paid an income that puts her on the budget line PQ, then she can access her old utility level denoted by IC1, although she now prefers the consumption bundle R which contains relatively more of clothing over food reflecting the substitution effect. Thus she will be indifferent between accepting the offer and staying back at Adelaide. Assuming to be the price of food in Melbourne, the required level of new nominal income is = II. Alternatively, Susan could be paid an income that allows her to access her old commodity bundle if she so desires. This is known as the Slutsky compensation. Essentially, the idea is that Susan will be back to her previous level of real income if she can purchase her old bundle if she wants. This would imply putting her on a budget line that passes through her old bundle E. This is shown in the diagram below: Figure 6: The Slutsky compensation - UV is the budget line that allows Susan to buy her old bundle E if she so desires. UV is the budget line that puts Susan at a real income level that is equal to her real income level at Adelaide according to this method, since she can once more purchase her old commodity bundle. However, an important point to observe from figure 6 is that although Susan has the option of purchasing her old bundle, she now can attain a higher level of utility IC2 by picking the bundle R. Susan’s required nominal income level in order for her to be indifferent between her present employment and the job at Melbourne is Comparing cases I and II, we find that the absolute minimum that has to be paid to Susan to ensure she accepts the job at Melbourne is , which is the amount required to ensure she can retain her initial utility level. The final point to note is that while Susan’s nominal income will be higher in Melbourne compared to her nominal income in Adelaide, her real income measured in terms of utility level is unchanged. However, it can be argued that her real income is lower since although she can attain her previous level of utility, she cannot attain her initial commodity bundle. The final say regarding the comparison of real incomes is a matter of perspectives. If we believe that real incomes are measured in terms of utility, then she has the same real income as before. If we believe that real incomes are measured in terms of commodity bundles, then her real income is lower. Question 2 Case i) The cost minimizing condition is --------- (1) Since the firm is required to produce 1000 units, the isoquant is represented by the equation: -------- (2) Using (1) in (2), we obtain: Again, using the value of L obtained in (3) in equation (2) we arrive at K= Therefore, the minimum cost attainable for producing 1000 units of output using production technology specified as i), is (10 x 122.47)+ (15 x 81.65)= 2449.45 Now, consider case ii) Q=2K+L Observe that here capital and labour are perfect substitutes. Therefore, in equilibrium investing all resources in either input will be optimum. i.e., there will be a corner solution. There are two possibilities that must be explored: a)all resources invested in capital and b) all resources invested in labour. Consider table 1 where we show how producing the entire output using only capital is cheaper. Table 1: Costs of producing 1000 units when either of the inputs are used Capital Labor Total Cost 0 1000 10000 500 0 7500 Thus, we find that the cost minimizing input combination using technology specified as ii) is K=500, L=0. This implies a total cost of 7500. Thus, we find that using technology i) is cheaper. It can produce 1000 units of output at a minimum cost of 2449.45 where as the minimum cost of producing 1000 units of output using the perfect substitutes technology, is 7500. Thus we can conclude that the firm will choose as its production technology. Question 3 Part (i) Figure 7: Edgeworth Box diagram of the two producers producing the identical output of the same goods, x=labour, y=energy Figure 7 is the required diagram. The isoquants of the two producers are tangent to one another exactly at the centre of the square. The isocost line (the dotted diagonal) is also tangent to the two isoquants at this point. Observe that producer 1’s equilibrium input choice of labour x=x1=x2=producer 2’s equilibrium choice of input x and similarly the equilibrium choices of energy y1=y2. It has also been assumed that the two isoquants correspond to the same levels of output q1=q2=q. Part (ii) Figure 8: If the budget remains unchanged,then the production set for both firms shrinks In figure 8 above, we first show the impact that the changed relative input prices has on the production set if the total resources of the firms stays the same. The increase in the price of electricity resulting from the carbon pricing regime leads to a reduction in the amount of energy that can be used if all resources of the firm are invested in purchasing energy. Thus, the budget line pivots around point B and swings down to BC from the initial AB. BC reflects the new relative prices. If the firms intend to retain their previous levels of output then they will have to attain their previous isoquants at the new relative price ratio. This requires an outward shift of the new budget line BC so that either the old combination of inputs becomes available or the old iso-quant is attainable again. Figure 9: Required increases in the budget for firm 1 and firm 2 to attain initial output level q Figure 9 shows the cost implications of producing the previous level of output at the present relative input prices. For firm 1, shifting out the budget line to EF does the job. Observe that from budget line EF, the old iso-quant (denoting output level q1=q) is attainable again. However, for firm 2, the required shift of the budget line is greater. The budget set has to increase to GH which lies above EF in order to attain the initial output of q2=q. Thus, we see that firm 1 is able to make a better adjustment compared to firm 2. The cause lies in the fact that while firm 1’s production technology allows for substitution between the two inputs, firm 2’s does not (it uses a fixed-proportion-of-input technology). Thus, when the price of energy rises, firm 1 is able to save some money by substituting in labour for energy. This is not an option for firm 2 since it has to use both inputs in fixed proportions. As a result, firm 2 can attain its initial level of output only if it can attain its initial input combination which has become relatively more expensive. Read More