The Utility Maximizing - Coursework Example

Assignment 3 Chapter 5 Applied problem1.As per the given problem (Thomas & Maurice, pp. 160-192), the information we have about Bridget’s food consumption and related factors is summarized in the table below: Units of Food MU(w) MU(w)/Pw MU(c) MU(c)/Pc 1 2 3 4 50 5 5 6 7 8 9 10 40 10 Where MU(w) is the marginal utility at given level of consumption for wine MU(w)/pw is the marginal utility per dollar spent on wine MU(c) is the marginal utility for cheese at a given unit of consumption MU(c) is marginal utility per dollar spent on cheese It is clear, as of now we do not have the complete information that is required, however: a. Bridget is not making the utility maximizing choice as of now, since the decision regarding the chosen quantities of cheese and wine are not based on the limited income she has. The quantities chosen do not anyhow relate to a specific limited income figure for Bridget. Also, the information regarding the limited income and utility at various levels is incomplete as shown in figure above. It should be noted that as per the current choice of quantities for cheese and wine the marginal utility of wine per dollar spent is 5, whereas that of cheese is 10, which are not equal and thus more of substitution needs to take place for utility maximization. b. Bridget should first of all arrive at a figure as per her limited income as to the maximum amount she can spend on food. Next, she must determine the various amounts of utility derived from wine and cheese at various levels of consumption units. This will give requisite information as to the levels of consumption for both wine and cheese, where the marginal utility per dollar spent for both will be equal. This will give the combination of utility maximizing quantities. Chapter 6 Applied problem 1.As per the given problem (Thomas & Maurice, 2011, pp. 204-232), USA today does not agree with the analyst that a raise in unit price of the paper from 50 to 75 cents will bring in an additional $65 million revenue. In this case, the analyst is assuming that the demand for paper is relatively inelastic and increasing price will not cause the sales of copies to drop. However, the USA today itself, citing the example of Wall street Journal, rejects this observation. It does so based on the observation that the sales of wall street journal dropped sharply after an increase in the price per unit. In doing so, the paper assumes that Price elasticity of demand for the paper is the same as that of Wall street journal. In doing so, it implicitly assumes that the demand for the paper is highly price elastic. Chapter 7 Applied problem 1.As per the given problem (Thomas & Maurice, 2011, pp. 243-276) , the Wilpen company, is a price setting firm, which estimates its U.S. demand for Tennis balls using the following linear equation: Q=a+bP+cM+dPr……….(1) Where, Q is the number of cans of Tennis Balls sold quarterly, P is the wholesale price of a can of tennis balls, M is the consumers’ average household income and Pr is the average price of tennis Rackets. Based on the given information, a. The Parameter a, which is the Y intercept for the regression line for the function. As per the computer output given, the value of ‘a’ is 425120.00, which means that if explanatory variables P, M, and Pr are zero, the Quantity Q is equal to 425120.00. The t-value for â is 1.93 and the p values for the same is 0.0716, which suggests that the value of 1.93 is large enough to conclude that ‘a’ is not equal to zero at a significance level of 7%. The parameter ‘b’ is statistically significant by an absolute t-value of 22.96 at 0.93% level. The parameter ‘c’ is statistically significant by a level of 4.08 at 0.09% significance level. Parameter ‘d’ is statistically significant by a level of 3.16 at 0.6% significance level. ‘a’ is expected to be positive as per the theory of demand, since the quantity ‘Q’ demanded is likely to fall with the rise in absolute values of P, M and Pr. Also, b0 since an increase in M will cause the ‘Q’ to rise and has a direct relationship with ‘Q’. b. Number of Cans of tennis balls sold or demanded can be expressed as ‘Q’ and is given by the expression in equation 1. Substituting the coefficient values for from computer output, Q=425120+ (-37260.60) X P + 1.49 X M – 1456 X Pr Further, substituting the values of the explanatory variables, p, M and Pr as given, Q=425120+ (-37260.60) X $1.65 + 1.49 X $24,600 – 1456 X $110 =425120 – 61479.99 + 36654 – 160160 =425120+ 36654 – (160160 + 61479.99) =466174 – 221639.99 =244334.01 c. The Elasticity of demand and the variations are given as Price elasticity of demand (PEOD ) =(b^) X P/Q……………………..2 Income elasticity of demand (IEOD ) =(c^) X M/Q……………………..3 Cross price Elasticity of demand (PXR EOD ) = (d^ X PR /Q)………….4 Where b^, C^, and d^ are the coefficients of the explanatory variables in the equation 1, and Q is the Quantity demanded and P, M and PR are the explanatory variables as also explained above. Substituting the given values in 2,3 and 4 above, PEOD =37260.6 X 1.65/244334.01= 0.25………………………………5 IEOD =1.49 X 24,600/244334.01 = 0.15………………………………..6 PXR EOD =1456 X 110/244334.01 = 0.65……………………………….7 d. If the Price of Tennis balls decreases by 15%, the percent number of tennis balls demanded will increase as follows: PEOD = %∆Q/%∆P……………………………………………………………………….8 Thus, substituting (5) in (8), %∆Q=15% X 0.25=3.75% increase e. If the average household income increases by 20%, the percent number of tennis balls demanded will increase as follows: IEOD = %∆Q/%∆M…………………………………………………………………………9 Thus, substituting (6) in (9), %∆Q=0.15 X 20%=3% increase f. If the average price of Tennis Rackets increases by 25 percent, the percent number of tennis balls demanded will decrease as follows: PXR EOD = %∆Q/%∆PXR ……………………………………………………………….10 Thus, substituting (7) in (10), %∆Q=0.65 X 25%= 16.25% decrease References Thomas, C. R., & Maurice, S. C. (2011). Theory of Consumer Behavior. In C. R. Thomas, & S. C. Maurice, Managerial Economics (pp. 204-232). The McGraw-hill Companies. Read More