Explain Business + Mathematics = Economics
(1) The Jamison Company produces steel. Its demand curve is linear. Its current price and quantity are $237.50 and 1,050 tons, respectively. Management determines that if they lower the price to $200, they will sell 1,200 tons of steel.
a. Calculate the arc price elasticity between these two points on the demand curve.
b. Should management lower the price? Explain.
c. Use the information in the problem to derive the equation for Jamison's demand curve equation (i.e., the "inverse" demand curve).
d. Find the price that maximizes total revenue. What is the elasticity of demand at this point? What is the total revenue?
e. Jamison's marginal costs are $100/ton. Find Jamison's profit maximizing output and price.
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(2) You have won a free ticket to see an Eric Clapton concert (which has no resale value). Bob Dylan is performing on the same night and is your next best alternative activity. Tickets to see Dylan cost $30. On any given day you would be willing to pay up to $50 to see Dylan. Assume there are no other costs of seeing either performer. Based on this information, what is the opportunity cost of seeing Eric Clapton? Explain.
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(3) Suppose that it takes the following number of hours to produce cheese and wine in Holland and Italy. Assume that (a) there are 24 hours to allocate in each country,
(b) currently there is no trade between Holland and Italy, and (3) each country currently allocates 12 hours to each product.
Cheese (1 lb.)
Wine (1 gallon)
Holland 1 hour 2 hours
Italy 6 hours 3 hours
a. How much wine and cheese is being produced in each country? Show how the combined production of cheese can be increased while holding the combined wine production constant.
b. Which of the two countries has an absolute advantage in producing wine? Which has a comparative advantage in producing wine? Explain.