COBECON Term 2 AY 2021-2022 Problem Set 2 (50 pts) Instructions: 1. Problem sets are to be submitted individually but you can answer with your classmates. It is advisable that you work on the problem sets alone, and then just check with the others. Grades are on an individual basis. 2. Read the questions carefully and answer only what is required. Show complete solutions, incomplete solutions will not be credited. For final answers that involve decimal places, round off to the nearest 2 decimal places. Box your final answers. 3. Solutions should be neatly hand-written only on one side of any type of clean paper (short bond, long bond, yellow pad, etc.). Make sure that your solutions are presented and organized as clean as possible. 4. Problem sets should be submitted in PDF format and uploaded in the respective assignment section in AnimoSpace. Submissions made elsewhere and type-written will not be accepted. For numbers 1-3, consider the following problem (24 pts): The table below shows total utility for two products. Suppose that the price for product A is $5 and the price for product B is $5. Also, the consumer has $25. Quantity of product A Total Utility for A Quantity of product B Total Utility for B 0 0 0 0 140 - 180 2 260 2 340 360 3 460 4 440 4 520 600 5 540 1. (20 pts) Given the data, complete the table below Marginal Marginal Marginal Utility for A Marginal Utility for B Quantity of A Utility for A per dollar Quantity of B Utility for B per dollar 0 0 1 W N . W N 4 4 2. (2 pts) How many units of product A should the consumer buy to maximize his/her happiness given the budget constraint? Why? 3. (2 pts) How many units of product B should the consumer buy to maximize his/her happiness given the budget constraint? Why?For number 4, consider the following problem (10 pts): Suppose a consumer wants to maximize utility given a Cobb Douglas utility function of U (x. y) = 361537025 and a budget line equation of I = Pxx + Pyy . The consumer has an income of $90, and that the price of good x is $2 and price of good y is $4. 4. Solve for the consumer's demand for each good and the utility. Show complete solutions. For number 5, consider the following problem (10 pts): Suppose a producer wants to minimize cost given a cost function of TC = wLL + wKK and a Cobb Douglas production function of Q(K, L) = K2/3L1/3. The producer has to produce 20 units output, and that the price of capital is $10 and price of labor is $5. 5. Solve for the producer's input for labor and capital, and the total cost. Show complete solutions. For numbers 6-10, consider the following problem (6 pts): 6. (2 pts) The table below shows data for product C of an individual rm. Complete the table. Quanti of roductC Fixed Costs FC Variable Costs VC Total Costs TC _Ii_ _Ii_ \"\" m- _i_ n . .- __ 7. What are xed costs when quantity is 0? 8. What are variable costs when quantity is 0? 9. What are variable costs when quantity is 3? 10. What are total costs when quantity is 7? EQUIMARGINAL PRINCIPLE A Consumer's Indifference Curve Equimarginal Principle: C Marginal utility per price on a good is exactly the same as the marginal utility per price on another 6 good. 5 Consumers will choose a combination of goods to AC 4 maximize their level of happiness Clothing B The Equimarginal condition can be represented 3 AF G as: 2 D MUC MUF MUX Slope = = Pc PF PX F 2 4 5 6 0 1 3 FoodMARGINAL RATE OF SUBSTITUTION Marginal rate of substitution: - Amount of a good the consumer is willing to give up to consume more of another good, at the same satisfaction level. - Marginal rate of Substitution of Good x for Good y: AY MRS\EQUIMARGINAL PRINCIPLE EXAMPLE: # of (Large size) Marginal Utility (Peppermint MU/P Marginal Utility MU/P cups Mocha Frap) (price = Php 180) (Matcha Milktea) (Price = Php 120) 1 st 1260 7 1200 10 2nd 900 5 720 6 3rd 540 600 5 4th 360 2 480 4 5th 270 1.5 120 1BUDGET CONSTRAINT The Budget line/constraint: I graphical representation ofthe consumers' budget. ' Each point represents a combination of the two goods, given an income and prices. - The budget line equation is given as: I: PxQx+PYQY PX Slope E . Points inside the budget line: Feasible set. \fSTEPS IN SOLVING UTILITY MAXIMIZATION (NON-CALCULUS APPROACH BY VARIAN) Example: Suppose that a consumer has the utility maximization problem U(x, y) = x2y3 s. t. I = Pxx + Pyy The consumer has an income of Php 100, and that Px = 1 and Py = 1. Solve for the consumer's demand for each good and the utility. Step 1: Set MRS = Price ratio Step 2: Substitute into budget constraint Step 3: Plug-in values to the utility function U(x, y) = x2y3 = (40)2 (60) 3 = N/W MRS = 2y Px y = : 3.456 x 108 utils 3x Py 100 = xty = x+ NI W -X = X 2y = 3x - y = NIW - X Solving for x: 100 x* = : 40 5/2 Marshallian Consequently, Demands y* = = (40) = 60UTILITY MAXIMIZATION Utility maximization problems in Economics (formally): U(x, y) = F(x, y)- - Utility function subject to I = Pxx + Pyy- Budget Constraint Utility functions can be: Cobb Douglas: U(x, y) = xaxy 'y; ax and ay parameters for x and y respectively. Substitutes: U(x, y) = axx + ayy; ax and ay parameters for x and y respectively. Complements: U(x, y) = min{axx, ayy}; ax and ay are parameters for x and y respectively. NOTE: Solving this problem requires knowledge of Differential Calculus. But we are not going to do that here