Economics calculation
d. (8 points) Using the Slutsky decomposition, calculate the substitution and income effects for the price change in part (d). Again, express your answer in terms of price(s) and income 4. Production (15 points) A firm faces the CES production function q = f(k, () = (10.5 + 10.5)15. Answer the following questions about this production function: a. (4 points) Does this production function exhibit increasing, decreasing or constant returns to scale? Show why. b. (4 points) Find the slope of an isoquant for this production function. 1 1 S. c. (2 points) Is this function homothetic? Why?3. Slutsky Decomposition (20 points) The utility function for an individual is given by U(X, Y) = X-25y.75. Prices for the two goods are Py and P, respectively, and income is I. The uncompensated demand functions for the two goods X and Y' are: a. (6 points) Derive the compensated demand function for good X, X"(Px, Py,I). b. (3 points) Are good x and y net (Hicksian) substitutes or complements? Show why. c. (3 points) For a small increase in the price of ) , what is the total change in the quantity demanded of X ? Express your answer in terms of price(s) and income. d. (8 points) Using the Slutsky decomposition, calculate the substitution and income effects for the price change in part (d). Again, express your answer in terms of price(s) and income.c. (4 points) What is the uncompensated own-price elasticity of demand for cheese? - rb d. (6 points) What is the compensated own-price elasticity of demand for cheese? 3. Slutsky Decomposition (20 points) The utility function for an individual is given by U(X, Y) = X-25y.75. Prices for the two goods are Py and P, respectively, and income is I. The uncompensated demand functions for the two goods X and ) are: a. (6 points) Derive the compensated demand function for good X, X"(Px,Py,I). 2/2. Utility Maximization (20 points) Bob gets utility only from cheese sandwiches, but he only likes to eat 2 slices of bread for every 3 slices of cheese. Please answer the following questions about Bob's consumption: a. (6 points) Write Bob's utility function for cheese and bread, U(c,b) (units are slices). Draw the indifference curve for U=2. Be sure to label all relevant points and be consistent with your definition of U(c,b). b. (4 points) Find Bob's demand for cheese (in slices) as a function of prices and income. c. (4 points) What is the uncompensated own-price elasticity of a.. d. (6 points) What is the compensated own-price elasticity of demand for cheese?1. Preferences and Utility (10 points) a. (2 points) Which of the three axioms of rational choice (completeness, transitivity, or rationality) would explain the fact that people can make up their minds about the relative desirability of any two alternatives? b. (8 points) Are the following utility functions quasi-concave? Show why. i(3 ) U(x, Y) = In(X) + Inin (5) u(x, Y) = min(X, Y) (Hint: You can use a diagram or sample values here)
