Preferences are quasi-linear and convex, and x is a normal good.
Preferences are homothetic.
Preferences are homothetic and convex.
Goods x and y are perfect substitutes.
With some services, e.g., checking accounts, phone services, or pay TV, a consumer is
offered a choice of two or more payment plans. One can either pay a high entry fee and
get a low price per unit of service or pay a low entry fee and a high price per unit of
service. Suppose you have an income of $100. There are two plans. Plan A has an entry
fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40 with a price of $1
per unit of using the service. Let x be expenditure on other good and y be consumption
of the service.
Write down the budget equation that you would have after you paid the entry fee for
each of the two plans.
With some services, e.g., checking accounts, phone services, or pay TV, a consumer is
offered a choice of two or more payment plans. One can either pay a high entry fee and
get a low price per unit of service or pay a low entry fee and a high price per unit of
service. Suppose you have an income of $100. There are two plans. Plan A has an entry
fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40 with a price of $1
per unit of using the service. Let x be expenditure on other good and y be consumption
of the service.
If your utility function is xy, how much y would you choose in each case?
With some services, e.g., checking accounts, phone services, or pay TV, a consumer is
offered a choice of two or more payment plans. One can either pay a high entry fee and
get a low price per unit of service or pay a low entry fee and a high price per unit of
service. Suppose you have an income of $100. There are two plans. Plan A has an entry
fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40 with a price of $1
per unit of using the service. Let x be expenditure on other good and y be consumption
of the service.
Which plan would you prefer? Explain.
Write an equation that describes Patience’s budget.
If Patience neither borrows nor lends, what will be her marginal rate of substitution
between current and future consumption?
If Patience does the optimal amount of borrowing or saving, what will be the ratio
of her period 2 consumption to her period 1 consumption?
A competitive firm has a production function described as follows. “Weekly output is
the square root of the minimum of the number of units of capital and the number of
units of labor employed per week.” Suppose that in the short run this firm must use 16
units of capital but can vary its amount of labor freely.
Write down a formula that describes the marginal product of labor in the short run
as a function of the amount of labor used. (Be careful at the boundaries.)
A competitive firm has a production function described as follows. “Weekly output is
the square root of the minimum of the number of units of capital and the number of
units of labor employed per week.” Suppose that in the short run this firm must use 16
units of capital but can vary its amount of labor freely.
If the wage is w=$1 and the price of output is p=$4, how much labor will the firm
demand in the short run?
A competitive firm has a production function described as follows. “Weekly output is
the square root of the minimum of the number of units of capital and the number of
units of labor employed per week.” Suppose that in the short run this firm must use 16
units of capital but can vary its amount of labor freely.
What if w=$1 and p=$10?
A competitive firm has a production function described as follows. “Weekly output is
the square root of the minimum of the number of units of capital and the number of
units of labor employed per week.” Suppose that in the short run this firm must use 16
units of capital but can vary its amount of labor freely.
Write down an equation for the firm’s short-run demand for labor as a function of w
and p.
Write an expression for the firm’s profits as a function of ticket price and
expenditure on players.
Find the ticket price that maximizes revenue.
Find the profit-maximizing expenditure on players and the profit-maximizing
fraction of games to win.
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