part 4 5 6 Question 1. In this question we begin by constructing a competitive market for a good, and then compare theoutcome when supply is controlled by a single-price monopolist. Suppose that the demand for units of somebeverage comes from households with the preferences over units of the beverage (x,) and expenditure on allother goods (x2) represented by the following utility function,U(x1, x2) = 800 In(x1) + x2Each household has an exogenous income of I per period. The second 'good' is referred to as a 'composite'good and is an amount of money. We assume throughout that p2 = 1.i)Derive a household's ordinary demand functions, x, (P, 1,1) and x,(P1, 1, 1) when theyare price-takers in the market for the beverage. How large does the exogenous income need to bein order for the household to enjoy a positive amount of both 'goods'?ii)Suppose there are 80 households who participate in the market for the beverage. Half ofthe households have an income of $1200 per period, and the other half have an income of $3000per period. Find the market demand function for the beverage.iii)The market is supplied by two types of firms with the following cost functions,C^(x) =x2 and C (x) =x.10,00010,000Find each type of firm's supply function if we treat them as price-takers.If there is one firm of each type, find the market supply function using your answer in iii)."Calculate the market equilibrium price and quantity.Use your answer in v) to find the profits of each firm type.Illustrate the market equilibrium using a sketch of the supply and demand functions.If the market was instead supplied by a monopolist with the cost functioniv)v)vi)vii)vii)C(x) = r2,40,000can you find a profit maximizing choice of output? Explain.If the monopolist had the cost function C(x) -thousands of units of the good could be chosen (x = 0, 1000, 2000, 3000, .) by the monopolist,what amount would the monopolist supply then? Explain your reasoning.3ix)x², but only discrete blocks of40,000x)Compare the monopolist's profit maximizing choice in ix) to the market equilibrium youfound in v) using a sketch with the market demand and relevant supply-side curves. Identify thedeadweight loss (extent of inefficiency) arising from the monopolist's restriction of supply to themarket.

From previous parts we know , Demand function for x1 : x1* = 800/P1 Number of Families = 80 Total…

outcome when supply is controlled by a single-price monopolist. Suppose that the demand for units of some beverage comes from households with the preferences over units of the beverage (x,) and expenditure on all other goods (x2) represented by the following utility function, U(x1, x2) = 800 In(x,) + x2 Each household has an exogenous income of I1 per period. The second 'good' is referred to as a 'composite' good and is an amount of money. We assume throughout that p2 = 1. i) Derive a household's ordinary demand functions, x, (P,, 1,1) and x2(P, 1,1) when they are price-takers in the market for the beverage. How large does the exogenous income need to be in order for the household to enjoy a positive amount of both 'goods'? ii) Suppose there are 80 households who participate in the market for the beverage. Half of the households have an income of $1200 per period, and the other half have an income of $3000