I. COMPETITIVE MARKET EQUILIBRIUM In a competitive market, the demand and supply conditions are described by, respectively, the inverse equations p = 20 2 ng p = 2 + Q5: where p is the price of the good (in 3/ unit) and Q is the quantity that buyers and sellers would, respectively, trade at each price (in units of the good). 1. Determine the equilibrium (62*, p\") in this market. Explain. 2. Determine the buyers1 expenditure {or sellers' revenue) in equilibrium. Explain. II. ELASTICITY Demand for oranges in the local market is given by the demand equation q = 100 4 p, where q is the quantity demanded (in lbs.) and p is the price (in $ / 1b.). 1. Determine the price-elasticity of demand when the price of oranges increases from $2/lb. to $3/ lb. Interpret your result. 2. Suppose the price of oranges is $2 [113. and a change in the price of apples in the local market from $2.50 / basket to $3.50/ basket leads to a shift in the orange demand equation above to q = 110 4 p. Determine the cross price elasticity of orange demand. Interpret your result. III. INPUT CHOICE A pizzeria uses two inputs: a restaurant and labor. The owner rents the restaurant, which comes with everything (including a periodically re-stock pantry with all the raw materials and supplies). The owner only needs to add labor. So, she hires help to make the pizzas. She decides on the the number of hours of labor per week to hire. That is her "input choice" or "input demand decision." To inform her decision, based on her experience in the business, she considers the following data on different amounts of labor (hours/week) and pizzas produced: L (hours) Q (pizzas) 0 40 200 80 350 120 450 160 500 1. Determine the average product of labor for each input level. 2. Determine the marginal product of labor for each change in the input and output levels. L ( hours) Q (pizzas) AP, (pizzas/hour) | MP (pizzas/hour) 0 40 200 80 350 120 450 160 500 3. Graph the data with the input (labor in hours/day) on the horizontal axis and the output (pizzas/day) on the vertical axis.Suppose that, in the example above, the wage rate the owner pays the worker is u: = $40 / hour, and that such wage rate is constant [i.e. it is not affected by the number of hours of labor hired), and that the price of a pizza is p = $12/pie (Le. also constant, not affected by the number of pizzas she decides to produoe and sell in a given week). 4. What is the marginal revenue product of labor, MRPL? 5. What is the optimal level of labor input to hire, If\"? .. ($th