d. Are ribs a normal or inferior good? e. The price of ribs falls to 5$. Draw the income and substitution effects of this price change graphically. Assume ribs are on the horizontal axis.SECTION C: LONG ANSWER 3. Rahul and Juan are the only consumers in the market for root beer in a small town in Nova Scotia. Their demand curves are given by P-30-2Qi and P=60-20j, where Qi and Qj are the quantities demanded by Rahul and Juan, respectively. What is the market demand curve for root beer in their town? 4. Nadia likes pork Ribs (R) and Chicken wings (C). Her utility function is U(R, C) = 10RC. Her weekly income is $90 which she spends exclusively on R and C. The price for a slab of ribs is $10 and $5 for a piece chicken. (Answer parts a to f). a. State in words and in math Nadia's consumer problem b. What is Nadia's optimal bundle? C. What is her demand function for ribs?SECTION B: TWO TRUE/FALSE/UNCERTAIN statements. Justify why. The total effect of a price increase on its demand is smaller than the substitution effect 1. The government puts a price ceiling on the cost of a large pizza. Consumers will loose from this policy. 2. All goods, normal or inferior, satisfy the Law of Demand.3. (20) In Kydland and Prescott's original RBC model, they made the assumption that investment does not produce capital immediately; i.e. the economy exhibited "time to build". Consider a representative- agent (i.e. no population growth), non-stochastic version of their economy and assume that agents have preferences given by: Est (Ing + 0In (1 - h)) 1 = 0 where & is consumption and he is time spent in work activity. Aggregate output is produced using a standard Cobb-Douglas production function: where y is output and &, denotes capital. (Note that there is no technological progress in the economy.) In each period, agents choose consumption, work effort and investment in order to maximize lifetime utility. In this economy, an investment project started at time t does not produce capital until period t + 2. The costs associated with this project are spread out evenly over the two-period horizon. Hence, when an investment project is started at time t, the agent is committing to an equal expenditure in period t + 1. Let sy denote investment expenditures on a project that is finished after i periods (i = 1, 2). Then total investment expenditures at time t are given by: it = sit + $21 (1) The law of motion for the capital stock is given by: kit1 = ki (1 - 6) + sit (2) Given this environment, do the following: (a) Express the associated social planner problem for this economy as a dynamic programming problem. Be explicit in identifying the states and control variables in each period (along with the laws of motion for the state variables). (Note: it is easiest to write the law of motion for capital as an additional constraint. Also, note that because of the time-to-build feature, the price of capital will not be equal to 1. Let the shadow price of capital be denoted q.) (b) Derive and interpret the necessary conditions associated with an optimum. (c) Solve for the steady-state output-capital ratio, the investment-capital ratio, and the ratio of time spent in work activity to time spent in leisure as a function of the exogenous parameters. Also solve for the steady-state value of q. Interpret this result.1. (10) Consider the simple RBC economy studied in class in which the economy is populated by identical agents with log utility and the production function is Cobb-Douglas. The depreciation rate of capital is 100% and technology shocks are i.i.d. The equilibrium policy functions for consumption and capital are constant fractions of output. (You do not need to derive these; you may simply state them.) Suppose one-period real bonds are introduced into this economy. Working directly from the associated Euler equations, do the following: (a) Prove that the risk premium on capital is positive. (b) It is often argued that the marginal product of capital and the real interest rate should be positively correlated. Is that the case in this economy? Explain. 2. (20) Consider an exchange economy populated by identical agents that trade equity shares, at, defined as title to the endowment process. (That is, this is the same asset priced in the Lucas tree model.) Denote the price of equity as q. Agents also trade one-period bonds which cost p units of consumption in period t and return 1 unit of consumption in the following period. In addition to these assets, a one-period forward contract on bonds is traded. In this contract, agents agree at time t to pay d units of consumption in period + + 1 for the promise of one unit of consumption to be received in period t + 2. The endowment, It, is stochastic and varies over the interval (z, 7); furthermore, r, is assumed to be independently and identically distributed. Given this environment, agents choose a sequence of consumption and assets in order to maximize (a) Formulate the agent's problem as a dynamic programming problem. Be explicit in identifying the state and control variables. (b) Derive and interpret the necessary conditions which characterize the solution to this maximization problem. (c) Define a recursive equilibrium in this economy. How are rational expectations imposed in this context? (d) Prove that equilibrium bond and equity prices are positively correlated with the endowment while the price of the forward contract is constant. Explain these results