Question 1. In this question we begin by constructing a competitive market for a good, and then compare the 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(x1) + x2 Each 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,(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 per 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) =x and C"(x) =x. 10,000 10,000 Find each type of firm's supply function if we treat them as price-takers. iv) If there is one firm of each type, find the market supply function using your answer in i).
Question 1. In this question we begin by constructing a competitive market for a good, and then compare the 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(x1) + x2 Each 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,(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 per 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) =x and C"(x) =x. 10,000 10,000 Find each type of firm's supply function if we treat them as price-takers. iv) If there is one firm of each type, find the market supply function using your answer in i).
Chapter6: Demand Relationships Among Goods
Section: Chapter Questions
Problem 6.14P
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