Amy is a chocolate lover and has a total of 50 dollars to spend this week. The price of a certain brand chocolate is p dollars per box. Amy's preferences for buying q boxes of chocolate and leaving a nonnegative amount (50 - pg) in her bank account, are represented by the utility function: U(g) = v7 + V50 - pq. qE (1) Find the first-order condition for a utility-maximising quantity of chocolate box. (2) Solve the first-order condition derived in (1) in order to express the utility-maximising quantity q" as a function of p. (3) What condition will guarantee that your quantity q is really a maximum? (4) Express the elasticity of demand for chocolate as a function of the price p per box. When the price is 5 dollars per box, calculate the price elasticity of Amy's demand for

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