:Answer all questions.

An increase in price will result in no change in total revenue if:

A) the percentage change in price is large enough to cause quantity demanded to fall to zero.

B) the coefficient of elasticity is equal to zero.

C) the percentage change in quantity demanded is equal to the percentage change in price .

D) the demand function is perfectly elastic.

Assume the demand for a good is price inelastic, i.e., ed

This means that if price decreases by 50 percent, quantity demanded will: *

A) increase by more than 50 percent.

B) decrease by more than 50 percent.

C) increase by less than 50 percent.

D) decrease by less than 50 percent.

As the percentage of the consumer's income accounted for by a particular good decreases, demand for the good will:

A) tend to become more price elastic.

B) tend to become more price inelastic.

C) tend to become closer to unit elastic.

D) tend toward being perfectly elastic.

For an inferior good, the income elasticity of demand is:

A) positive or negative depending on the share of income accounted for by the good.

B) always negative

C) positive if income increases and negative when income declines.

D) always equal to 1.

Supply is best defined as the relationship between:

A) the current price of a good and the quantity supplied at that price.

B) the price of a good or service and the quantity supplied by producers at each price during a period of time.

C) the cost of producing a good and the price consumers are willing to pay for it.

D) the quantity supplied and the price people are willing to pay for a good.

Which of the following would cause a change in supply, as opposed to a change in quantity supplied, in the market for purchasing new homes?

A) A decrease in the price of rental housing.

B) A decrease in the price of new homes

C) An increase in the incomes of home buyers.

D) An increase in the number of buyers in the market for used homes.

Many people consider lentils to be an inferior good. For such people, all else held constant, an increase in income would cause their demand for lentils to:

A) increase.

B) stay the same.

C) decrease.

D) cannot be determined with the information given.

Suppose the demand for good X is given by Q_x^d = 300 - 15Px + 20Py - 60I , where Px is the price of good X. Py is the price of some other good Y, and I is income. Assume that Px is currently $50, Py is currently $100, and I is currently $1200

A) Goods X and Y are complement goods

B) The supply is elastic

C) Good Y is a normal good

D) Good X is an inferior good

The price elasticity of demand is calculated as:

A) the change in price divided by the change in quantity demanded.

B) the change in quantity demanded divided by the change in price.

C) the percentage change in price divided by the percentage change in quantity demanded.

D) the percentage change in quantity demanded divided by the percentage change in price.

Consider the following time-inhomogeneous Markov jump process with transition rates as shown below: 2 0.12 0.21 0.1/ 0.21 4 0.05r 0.5 (i) Write down the generator matrix at time /. [2] (ii) Write down the Kolmogorov backward differential equations for By(s,() and Pi3(s,1). [3] (iii) Using the technique of separation of variables, or otherwise, show that the solution of the differential equation for Pay(s,() is: By(s, !) =e [4] (iv) Show that the probability that the process visits neither state 2 nor state 4 by time /, given that it starts in state 1 at time 0, is: 8 -0.07512 1 -0.251- [6] (v) State the limiting value as / -> > of the probability in (iv). Explain why this must be the case for this particular model. [2] [Total 17]1. Assume that a decision maker's current wealth is 10,000. Assign w(0) = -1 and u(10,000) = 0. a. When facing a loss of X with probability 0.5 and remaining at current wealth with probability 0.5, the decision maker would be willing to pay up to G for complete insurance. The values for X and G in three situations are given below. X G 10 000 6 000 6 000 3 300 3 300 1 700 Determine three values on the decision maker's utility of wealth function b. Calculate the slopes of the four line segments joining the five points de- termined on the graph u(w). Determine the rates of change of the slopes from segment to segment. c. Put yourself in the role of a decision maker with wealth 10,000. In addition to the given values of w(0) and u(10,000), elicit three additional values on your utility of wealth function u. d. On the basis of the five values of your utility function, calculate the slopes and the rates of change of the slopes as done in part (b). 2. St. Petersburg paradox: Consider a game of chance that consists of tossing a coin until a head appears. The probability of a head is 0.5 and the repeated trials are independent. Let the random variable N be the number of the trial on which the first head occurs.Question 3 (20 points) Consider the social planner's problem for a real business cycle model. The house- hold makes consumption (C) and leisure (1 - N, where N is hours worked) decisions to maximize lifetime utility: Eo B'u (Ct, 1 - N.) (1) 1=0 Specific functional forms will be given below. Output is produced using capital K and labor N YI = Z, KPN)- (2) Z: is a TFP shock and is governed by a discrete state Markov chain. Capital evolves: Kit1 = (1 - 8)Ki + 1 (3) but assume full depreciation so 6 = 1. There is no trend growth. Finally, First suppose that the utility function u is as follows: In (C - ME (4) a) Write down the recursive formulation of planner's problem and derive the first order conditions. b) Using guess and verify, find the policy functions for investment, consumption and hours worked (Hint: first consider the equilibrium condition for hours worked and guess that investment is a constant share of output). Now suppose the utility function is given by: In Co - 2 (5) c) Repeat parts (a) and (b) using these new preferences. d) Compare the business cycle properties implied by these two models and explain how and why a TFP shock might affect output, consumption, investment and hours worked. Some RBC modelers prefer preferences used in parts (a/b) to those in part (c), why might this be the case? e) If 0