110年 - 110 國立臺北大學_碩士班一般入學考試試題_經濟學系：個體經濟學#146585

(a)(5%) What is the compensating variation when \( P_{x} \) increases from \( \frac{1}{3} \) to \( \frac{1}{2} \)?

(b)(5%) What is the equivalent variation when \( P_{x} \) increases from \( \frac{1}{3} \) to \( \frac{1}{2} \)?

(c)(5%) What is the income effect when \( P_{x} \) increases from \( \frac{1}{3} \) to \( \frac{1}{2} \)?

(a)(10%) What are the conditions in \( \beta \)'s to ensure that the translog cost function is homogeneous of degree one in \( w \) and \( r \)?

(b)(5%) What is the condition in \( \beta \)'s for the translog cost function to reduce to the constant elasticity cost function?

(a)(5%) Which column represents the demand side, if any?

(b)(5%) Which column represents the supply side, if any?

(c)(5%) What do you know about the cell labeled (c)?

(d)(5%) What do you know about the cell labeled (d)?

[Hint for (c) and (d): provide a range, for example "the number must be smaller than -1.00," when you do not know the exact number.]

(a)(4%) Suppose that KFF would never enter into the fish market. Find out McDaniel's optimal price for each good and monopoly profit.

(b)(5%) Suppose that McDaniel sells fish and chips separately (i.e., consumers can purchase only fish or only chips from McDaniel). Find out McDaniel's equilibrium profit after KFF enters into the market, and the value of \( F \).

(c)(6%) Suppose that McDaniel serves only a set menu, which consists of fish and chips, at a price \( p^M \), and so consumers cannot buy only fish or only chips from McDaniel. Find out McDaniel's equilibrium price \( p^M \) and profit after KFF enters into the fish market.

(d)(4%) Suppose that \( f = 2 \) and McDaniel only offers the set menu as in question (c). Find out the equilibrium profit of McDaniel and KFF, respectively, of the whole game.

(e)(4%) Find out McDaniel's monopoly profit (i.e., when KFF would never enter).

(f)(6%) Suppose that KFF has entered into the market, and McDaniel sells fish and chips separately. Let \( pA^K \) be KFF's price of fish, and \( pA^M \) McDaniel's price of fish and \( p_B^M \) McDaniel's price of chips. Find out prices and McDaniel's profit in Bertrand equilibrium.

(g)(4%) Suppose that \( f = 2 \) and McDaniel serves only a set menu. Find out McDaniel's profit in equilibrium of the whole game.

(a)(4%) Suppose that they can save or borrow at zero interest rate, which is close to current situation. How much, if any, would the father and son, respectively, optimally save or borrow in 2021?

(b)(6%) Suppose that they have no access to the financial market, but can make the following arrangement. The father gives the son an amount of $R in the red envelope in 2021, and the son gives the father some pocket money $P in 2022, where R and P ≥ 0 (a negative amount means the opposite flow of money). Describe all the Pareto optimal pairs (R, P), if any, that both would agree, and illustrate in a figure. (There is no need to compute the exact number.)

(c)(7%) Following the previous question, find out all the Pareto optimal pairs, if any, that could be implemented by the financial market (i.e., through private borrowing and saving when both are price-takers), and the corresponding interest rate.