[1] What are the "choice variables and what are the "parameters' in this problem? What is the difference between them? [2] How do we know this problem has a solution? [3] Explain the relevant Lagrangian function. [4] Explain the conditions that will characterize a KT-point. [5] Use the conditions in part [4] to find the optimal consumption bundle (r*, y), and the associated Lagrange multiplier X*. [6] Explain why z* and y* can be interpreted as "functions". [7] Find the partial derivative of z* with respect to each "parameter of the problem". [8] Explain the interpretation of each partial derivate you find in part [7]. [9] Find the "indirect utility function' V = u(x, y), and explain its interpretation. [10] Find the partial derivative of V with respect to M, and explain its interpretation.

7) Suppose that a consumer's marginal rate of substitution at her current chosen bundle is MUX /MUY = 4, but she is able to exchange X and Y at Px/PY = 3. Should she keep her current bundle,or can she make herself better off by trading at these prices? Which good will she buy, and which will she sell?

12) In the market for smartphones, the price elasticity of supply is +0.8, and the price elasticity of demand is -1.2. At equilibrium, price is $800 and quantity is 400000. (a) Assuming supply and demand are linear, reconstruct and draw the supply and demand curves. Label the intercepts. (b)To help consumers and phone-makers, the government proposes to subsidize smartphones by $80each. What are PB and PS after the subsidy? What is the new equilibrium quantity? Illustrate them on the same graph. (c) Calculate the change in consumer surplus, producer surplus, government expenditure, and dead weight loss and identify them on the graph.

Question One Jane and John are a new couple trying to make a future production plan together. Assume there exist two types of production they can conduct: Household Production (HP) and Market Production (MP). If Jane does household production, her production value is $20 per hour; if she does market production, her production value is $10 per hour. If John does household production, his production value is $10 per hour; if he does market production, his production value is $20 per hour. Both Jane and John can work 8 hours on workdays. a) Calculate Jane and John's possible production frontiers (PPFs) on a workday and draw them in two diagrams. b) Combine Jane and John's PPFs in the same diagram. If both of them conduct market production, only, what would be their combined PPF? Show it in the diagram. If they do wish to keep some household production, who should do it? Show this new PPF in the diagram. Is there a limitation on this new PPF? c) On the other hand, if both Jane and John conduct household production, only, what would be their combined PPF? Show it in a diagram. If they do wish to keep some market production, who should do it? Show this new PPF in the diagram. Is there a limitation on this new PPF? d) If Jane and John "pool" their production possibilities together and split these possibilities equally between household production and market production, what would be their new PPFs? Show them in a diagram. e) Is there a gain for Jane and John to collaborate? If so, show it in a diagram.

5. (6 points) Suppose when we look at the monthly sales of hamburgers & fries in the Devil's Den, we see that when CCSU increased the price from $7 to $13, the quantity demanded fell from 8,000 meals to 4,000 meals.

3) Illustrate the following utility functions by sketching indifference curves in the X,Y space: (Need not be to scale as long as the general shape is reasonable) (a) U(X,Y) = 2X + 3Y (perfect substitutes)(b) U(X,Y) = X1/2Y 1/2 (Cobb-Douglas) (c) Derive the expression for the Marginal Rate of Substitution for the utility functions above.

Two MSU fraternities, Phi Kappa Sigma and Phi Kappa Tau, are accustomed to each having 6 parties a month. Phi Kappa Sigma and Phi Kappa Tau are located close to each other on Bogue Street. These parties impose a negative externality on their other neighbors on Bogue Street. Suppose President Stanley decides that the socially optimal total number of parties on Bogue Street is 8 parties a month. The total benefits each fraternity derives from having a certain number of parties a month are given in the table below.

1. Analyze the estimated demand function by using the estimated coefficients to discuss the impact of each of the explanatory variables, P, CP, M, and PE, on the quantity of Maa mustard oil demanded. In discussing the impact, consider a one unit change in each variable while holding the others constant.

2. For each of the explanatory variables, P, CP, M and PE, calculate the respective demand elasticities for Hind Oil Industries’ product in the month September 2015. Remember to show all calculations. What additional information about Maa mustard oil do these values provide?

QUESTION 4 A firm uses two inputs x and y, and their profit function is P(x,y)=3xy-2x+y. Input x costs $2 each and y costs $1 each and they are constrained to spend a total of $100 on inputs.