HHelp me to solve the following questions.

1. Suppose the production function for the output produced by a rm is f (L,K) = 40143\"r 4K \"4, where L is labor and K is capital. 1. What is the marginal product of labor? What is the marginal product of capital? 2. Suppose the rental rate of capital in the market is r=2, the wage of labor is w=10, the price of output is p=1f3 and the amount of capital is xed at 16 units (i.e., the rm is maximizing a function of a single variable, L, since K is xed). Assuming that the rm acts to maximize prot (note that prot is given by H = p'j'hK) w*L r*K), how many units of labor should the rm hire? Show that both the rst and second order conditions for a maximum are satised. What is the associated optimal output level? 11. Suppose now that the capital stock is variable, but the rm is constrained (by its lenders) to spend no more than a total of C=400. Assume the rm chooses inputs to maximize production and all prices are as indicated above, how much capital and labor will it hire? How much will it produce and what are its prots? PHNT: Maximize output, L, K), subject to the constraint on total costs (C), where total costs equal the sum of the cost of employing capital and labor (i.e., C=400=10*L + 2*K). The following graph input tool shows the daily demand for hotel rooms at the Big Winner Hotel and Casino in Las Vegas, Nevada. To help the hotel management better understand the market, an economist identified three primary factors that affect the demand for rooms each night. These demand factors, along with the values corresponding to the initial demand curve, are shown in the following table and alongside the graph input tool. Demand Factor Initial Value Average American household income $50,000 per year Roundtrip airfare from San Francisco (SFO) to Las Vegas (LAS) $200 per roundtrip Room rate at the Lucky Hotel and Casino, which is near the Big Winner $250 per night4. A unit mass of kids are uniformly located on a street, denoted by the [0, 1] interval. There are two ice cream parlors, one located in r and the other is located in 1 - r, where r 0. Given the prices p and q for the ice cream in stores located at r and 1 -r, respectively, each kid buys one unit of ice cream from the store with the lowest total cost, which is the sum of the price and the cost to go to the store. (If the total cost is the same, she flips a coin to choose the store to buy.) (a) Compute the revenue for each firm, as a function of price vector (p. q). The revenue is price times the total mass of the kids who buy from the given store. (b) Assume that each store set their own price simultaneously and try to maximize the expected value of its own revenue, as computed in part (a). Write this game in normal form. (c) Compute the set of Nash equilibria. (d) Compute the set of rationalizable strategies.Problem 2 (50 pts) In the late 90s it was observed that the relative price of equipment (capital) has declined at an average annual rate of more than 3 percent. There has also been a negative correlation (-0.46) between the relative price of new equipment and new equipment investment. This can be interpreted as evidence that there has been significant technological change in the production of new equipment. Technological advances have made equipment less expensive, triggering increases in the accumulation of equipment both in the short and long run. Concrete examples in support of this interpretation abound: new and more powerful computers, faster and more efficient means of telecommunication and transportation, robotization of assembly lines, and so on. In this problem we are going to extend the Solow Growth Model to allow for such investment-specific tech- nological progress. Start with the standard Solow model with population growth and assume for simplicity that the production function is Cobb-Douglas: Y = K" L, ", where the population growth rate is = n. Similarly, just as in the basic model, assume that investment and consumption are constant fractions of output It = sY, and Ct = (1 - s)Y. However, assume that the relationship between investment and capital accumulation is modified to: Kit1 - Ke = qthe - 6Kt where the variable q, represents the level of technology in the production of capital equipment and grows at an exogenously given rate y, i.e. 24 = y. Intuitively, when of is high, the same investment expenditure