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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.
- 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.Please answerThe 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.
- 1. Demonstrate that ɛ = Ex,l + Ex,k Note that: aA /\ = Ək / k = Əl / 1 And Ex.l is the elasticity product of the factor l. Similar for the factor k. 2. Find the o of: (with the process) %3D x (L, K) = aLP + bKP)ɛ/p If p<1 and a = 1; b = 1 %3DIn the nonlinear function Y = ax ZC, the parameter c measures Multiple Choice O O O the percent change in X for a 1 percent change in Z. None of these options are correct. the elasticity of Y with respect to Z. ΔΥ/ΔΖ.An increase in the value of one variable results, on an average, in a corresponding increase in the values of the other variable Select one: a. Increased correlation O b. Positive correlation O c. Decreased correlation O d. Negative correlation
- 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?Ma1. Please give only typed answer. Assume the following expendiexpenditure function. (a) Interpret this function. In particular, what will happen to the optimal expenditure, if the consumer wanted to maintain a high level of utility? (b) Calculate Hicks demand for good 2. (c) Suppose that p1 = 1, p2 = 1 and that U = 28. Calculate and interpret the variation compensation if the price of good 2 increases by $1.Only typed answer