Suppose that the demand for units of some beverage comes from two types of household. They...

 

Transcribed Image Text:

Suppose that the demand for units of some beverage comes from two types of household. They have the following utility functions representing their preferences of a household over units of the beverage (x1) and expenditure on all other goods (x2), U4(x1, x2) = x1/2x2/2 and UB(X1, x2) = 500 In(x1) + x2 The households have exogenous incomes of I and Ig. The second 'good' is referred to as a 'composite' good and is an amount of money. We assume throughout that P2 = 1. (6 marks) For each household type, derive the household's ordinary demand functions, x, (P1,1, 1) and x2(P1, 1,1). You can assume that both household types i) have enough income to reach an interior solution. ii) (2 marks) Suppose there are 10 households of each type. Find the market demand function for the beverage. ii) (3 marks) If the market supply is provided by 16 identical firms with cost function, C(x) = 4x?. Find the market supply function. (2 marks) Calculate the market equilibrium price and quantity in terms of the households' exogenous incomes. iv) v) (3 marks) Suppose the exogenous incomes changed so that they became (IA + 100) and (IB - 100). Did aggregate income of the households change? Did the market equilibrium price and quantity change? If so, by how much? (2 marks) If we were to have a market model where the demand side was composed vi) of 20 households of only one household type (A or B), which type of household would allow the market demand to be expressed as a function of aggregate income, 201? vii) (6 marks) Explain this result by illustrating the effect of a change in income for each type of household (as in v)) using an indifference curve analysis for each household. Suppose that the demand for units of some beverage comes from two types of household. They have the following utility functions representing their preferences of a household over units of the beverage (x1) and expenditure on all other goods (x2), U4(x1, x2) = x1/2x2/2 and UB(X1, x2) = 500 In(x1) + x2 The households have exogenous incomes of I and Ig. The second 'good' is referred to as a 'composite' good and is an amount of money. We assume throughout that P2 = 1. (6 marks) For each household type, derive the household's ordinary demand functions, x, (P1,1, 1) and x2(P1, 1,1). You can assume that both household types i) have enough income to reach an interior solution. ii) (2 marks) Suppose there are 10 households of each type. Find the market demand function for the beverage. ii) (3 marks) If the market supply is provided by 16 identical firms with cost function, C(x) = 4x?. Find the market supply function. (2 marks) Calculate the market equilibrium price and quantity in terms of the households' exogenous incomes. iv) v) (3 marks) Suppose the exogenous incomes changed so that they became (IA + 100) and (IB - 100). Did aggregate income of the households change? Did the market equilibrium price and quantity change? If so, by how much? (2 marks) If we were to have a market model where the demand side was composed vi) of 20 households of only one household type (A or B), which type of household would allow the market demand to be expressed as a function of aggregate income, 201? vii) (6 marks) Explain this result by illustrating the effect of a change in income for each type of household (as in v)) using an indifference curve analysis for each household.

Answer rating: 100% (QA)

There are two types of households A and B The type A has UA x112x212 and the type B has UB ... View the full answer