(a) (b) (c) 'Write down Tom's budget constraint. Write down Tom's optimal consumption-leisure tradeoff condition. Solve for Tom's optimal hours worked and optimal consumption.
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- Why does a change in income cause a parallel shift in the budget constraint?2. What is the economic interpretation of the condition that the consumer at his optimum equates his marginal rate of substitution and the price ratio of the goods he consumes?3. Draw and describe analytically the set of feasible consumption choices. What is the marginal rate of substitution at the optimal choice?
- 7. An individual's utility function is given by U =1000x, +450x, +5 x,x, -2x - x where x, is the amount of leisure measured in hours per week and x, is income earned measured in cedis per week. Determine the value of the marginal utilities, when x, = 138 and x, = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?6) The figure below shows a student's feasible frontier and her indifference curves for final exam marks and the hours of free time per day. The table also gives the marginal rate of substitution (MRS) and the marginal rate of transformation (MRT) for the points shown in the figure. Based on this information, identify whether each of the following statements is true or false. Final grade 100 c. At D, the MRT of 4 means that if she gives up all of her free time, she can attain 60 extra grade points. d. At E, the MRS matches the student's MRT. Therefore, she should exchange one hour of free time with 7 extra grade points. 90- a. At A, one hour of free time is equivalent in value to 3 grade points. However, 1 extra hour of studying leads to 9 extra grade points. She should therefore study more. 0 b. At B, one hour of free time is equivalent in value to 2 grade points. However, 1 extra hour of studying leads to 20 extra grade points. She should therefore study more. 0 Feasible frontier…Problem Set 1. A firm's production function is º=50L-0.01Ľ' , where L denotes the size of the workforce. Find the value of MP in the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form A P = Q" where A and n are positive constants. 3. The demand and total cost functions of a good are respectively 4P+Q-16=0 and ТС %3D 4 + 20 — 10 20 a) Find expressions for TR, (profit) 1 , MR, and MC in terms of Q. b) Solve the equation dn = 0 ÕP and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢'/, million per floor (e) Specialized costs of GH¢10000× per floor. How many floors should the office complex contain if…
- 1. An individual derives utility from the consumption of a basket of goods, c and leisure time, given by U(c, l) =cºl(1-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L + l = 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given. (a) Solve for the optimal labor supply.1. Suppose you consume two goods: x and y. Your marginal utility of x is 20 and your marginal utility of y is 24 at your utility-maximizing combination. The current price of x is $5. (a) What is the marginal rate of substitution at your utility-maximizing combination? (b) What is the price of y at your utility-maximizing combination?1.In income substitution effects acts in opposite direction, then the total effect on consumption is always negative. (T/F)
- 4.An individual consumes products X and Y and spends $30 per time period. The prices of the two goods are $3 per unit for X and $3 per unit for Y. The consumer in this case has a utility function expressed as: U(X.Y) = 0.5XY How much X should this individual consume, given that he is maximizing the utility? ( A) 4.17 ( B) 5 (C)6 D) 6.252. [For this question, the unit used is in thousands of Rupiah].Rihana's preferences for consumption (C) and leisure (L) are explained by the utility function:U(C, L) = (C - 200) (L - 56) so the marginal rate of substitution is MRS = (L - 56)/(C - 200) If Rihana has 168 hours to devote her time to work or leisure per week and she receives Rp. 240 of the pension fund per week, how much is Rihana's reservation fee? (A). Rp. 0(B). Rp. 2.80(C). Rp. 5.00(D). Rp. 6,25(E). Minimum wage rate. Choose one of the answers from the five choices provided. And please, also provide a brief description, explanation or argument for your choice. Thank you Bartleby!1. Refer to graph (multiple choice) graph represents Cara's budget constraint and preferences A. Refer to Graph, Which of the statements below is the most accurate? a. At point A, Cara's marginal valuation of leisure is higher than the market wage b. At point B, Cara's marginal valuation of leisure is higher than the market wage. c. At point B, Cara values leisure the same amount as at point A. d. At point A, Cara's marginal valuation of leisure is higher than the market wage, and at point B, Cara values leisure the same amount as at point A. B. Refer to Graph, At point A, Cara’s marginal rate of substitution of leisure for income a. exceeds the wage and Cara would like to work fewer hours. b. is less than the wage and Cara would like to work more hours. c. exceeds the wage and Cara would like to work more hours. d. is less than the wage and Cara would like to work fewer hours. C. Refer to Graph, Based on the graph above, we can conclude that a. Cara does not have…
