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- O let y= F(,k) = 2Č K be a pretustion funtion e ue told daivanve, to deniue, TRS this praquition fumition duplay mmu kinMartin a prequct in ? Hene about in k?. On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according to thefunctionU (c, b) = 20c - c2 +18b- 3b2.How many cigars and glasses of brandy does he consume during an evening? (Cost is no objectto J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum of glasses ofbrandy and cigars consumed to 5. How many glasses of brandy and cigars will he consumeunder these circumstances?Increase in the price of insulin doesn't effect its Qd whereas a slight increasein price of perfume drops its Qd to zero. Explain.
- What is Nature of a Dummy Variable?2. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility.4. Verify that a homogenous function has IRS, CRS or DRS depending on whether the degree of the function satisfies y> 1, y = 1, or y< 1.
- The rate at which a consumer must give up y to get one more x is equal to * 2 points a)-MUx/MUy. b)-Px/Py. c)MUy/MUx. d)-Py/Px.You decide to sell pairs of running shoes. Assume that the quantity demanded is alinear function of the price. It is known that if you charge $40 per pair of shoes, thenyou will be able to sell 400 pairs of shoes in a month. If you charge $60 per pair ofrunning shos, then you can sell 300 pairs of shoes in a month. It is also known thatyour monthly fixed cost is $100 and pairs of shoes cost $20 per shoe to produce. Findwhat price you should charge for a pair of shoes in order to maximize profit in amonthWhat is meant by dummy variable and how dummy variables are constructed?
- Please explain two principal variables that have determined the commodification by giving examples.3.Exercise 3 An individual lives two periods, 0 and 1. The income is 14,000 in period 0 and 5,000 in period 1. The individual's marginal utility is: K- Co in period 0 and d8(K – C1) in period 1, where C is the consumption in period 0, C1 the consumption in period 1 and d a discount rate. K is a constant (higher than the consumption in each period). Suppose that the person can save or borrow from the bank from period 0 to period 1 with a 25% interest rate. Set the discount rate & to 0.8. a) How much will the individual consume in the two periods? How much will she save? b) A National Insurance scheme (pension system) is established. The individual must pay 4,500 in period 0 and receives the same amount with interests in addition to her income in period 1. What will the consumption and savings be in the two periods if the National Insurance scheme uses the same interest rate as the bank?
