II. Given a translog cost function TC = β0 + β1 Q + β2 w + β3 r + β4 ( Q)^2 + β5 ( w)^2 + β6 ( r)^2 + β7 ( w)( r) + β8 ( w)( Q) + β9 ( r)( Q), where $Q$ denotes output, and $w$ and $r$ denote the prices of input $L$ and $K$, respectively. Answer the following questions: (a)(10%) What are the conditions in β's to ensure that the translog cost function is homogeneous of degree one in w and r?

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.

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