Following the analysis of the May and June data, the firm set its price at $5,000 for all of its customers. The client notes that August is a very good month because its product benefits from students going back to school. To gain information about this possibility, and its potential effect on demand, the consulting firm proposes that its client run an experiment by randomly raising its price to $5,125 for half of its customers. The Table below includes data for the months of July and August. Group A-No Price Change Group B-Price Changed Month July Price Quantity Price Quantity $5,000 800 $5,000 800 August $5,000 850 $5,125 825 Is the increase in the quantity sold to Group A the result of a change in demand, a change in quantity demanded, or a combination of these two effects? Explain Is the increase in the quantity sold to Group B the result of a change in demand, a change in quantity demanded, or a combination of these two effects? Explain Estimating a firm's price elasticity of demand requires that the analyst isolate the effect of a change in price on quantity demanded, holding all other factors constant. Because the change in prices were random, comparing the changes in prices and quantities for the two groups should provide the information needed to isolate the effect of a change in price on quantity demanded in this market. Explain how you can use the data provided above to estimate the firm's price elasticity of demand for the month of August. Assume that the consultant's client has a linear demand curve. Use the data to estimate the firm's price elasticity of demand when price equals $5,000 in August. Repeat the exercise for the case where the price equals $5,125. Show your work and verbally explain how you arrive at your estimates. - Use the equation that gives the relationship between price, price elasticity of demand, and marginal revenue, MR = P(1+(1/e)), to calculate the firm's marginal revenue when August prices equal $5,125 or $5,000. If the firm's marginal cost of production equals $1,000 per unit, and is constant, what price maximizes the firm's profit in August? Explain.