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

III. Given the table of a specific labor market below with some missing information. | Change in equilibrium wage | Change in tertiary-educated population | Change in technology | | --- | --- | --- | | - 0.53 | 3.19 | 2.41 | | -(c) | 2.35 | - 0.25 | | 0.79 | 2.91 | 4.08 | | 0.66 | 2.55 | - 3.52 | | - 0.70 | (d) | 3.95 | | 1.43 | 2.53 | 4.65 | Answer the following questions: (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.]

IV. A hundred identical consumers eat fish (good A) and chips (good B) for lunch. Each consumer eats at most one unit of each good, and the benefit of consumption is $20 for fish and $12 for chips. Currently McDaniel is the monopoly firm of both fish and chips, with constant marginal costs $5 for fish and $4 for chips. Kenting Fried Fish (KFF for short), whose fish tastes just as good as McDaniel's, is considering to enter into the fish market (but not the chips market). Consider a dynamic game where the KFF first decides whether to enter, and if yes, the two firms engage in Bertrand competition. If not enter, KFF earns zero profit, and McDaniel maintains monopoly. Entry requires a fixed cost $f; after entry, the marginal cost of KFF is $3, also constant. Let $F be the maximal value of entry cost that KFF is willing to spend. Suppose that, if the two firms charge the same price for fish, then all consumers will buy from KFF. For the next four questions, the consumption values of the two goods are independent. That is, eating fish has a benefit of $20, whether the consumer eats chips or not; similarly for chips. (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.

For the remaining three questions in this part, consider fish and chips as perfect complements. That is, a consumer obtains the consumption benefit of $20 for fish and $12 for chips only if he eats both fish and chips. For other consumption behaviors (eating only fish, only chips, or nothing), the consumption benefit is zero. (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.

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