Economic Issues
Directions: Answer all the following questions. Make sure to show all work and any formulas or graphs needed in the solution. All the solutions should be put in your solutions document. You may modify this word document and put all solutions on it. Make sure to start each question on a new page.
Questions:
1.Sometimes firms conduct experiments where they temporarily change prices (this may be done with selective coupons and other discounting methods) to see how the consumer responds to a price change. Let’s assume that our firm charges $15 per unit of output and on average has 400 units sold per day. However, for the last week the firm offered a $5 discount and charged only $10 per unit of output. During the week of the discount the firm observed that the average daily sales were 1000 units.
(i) Given the price and quantity information, calculate the Elasticity of Demand for the product.
(ii) What type of good/service is this (inelastic, elastic, etc.)? Explain.
(iii) Interpret your elasticity calculation.
Bonus: Part (iv) and (v) are considered bonus.
(iv) If we operate under the assumption of ceteris paribus, what is the best linear representation of the demand faced by the firm [please provide the equation for the demand in terms of Q = f(P)]. Hint:This is just solving for the equation of the line…so solve for slope and intercept.
Recall that to get the equation of a line we can choose one point and note:
(Y – Y1) = M(X – X1) à in this case your point would be (X1, Y1) à (P,Q) where M =
(v) If we continue to operate under the assumption that the demand is linear, what prediction can you make about the firm’s level of sales at the price of $8? Use your solution to predict this.
- Assume that the demand for product X is represented by the following equation:
QDx = 400 – 5Px + 4Py -3Pz. When asked to calculate cross-price elasticity for part iii for Q2, use Px=30 from the first part of the problem.
- i) Calculate the elasticity of demand if Px = 30 Py = 25 and Pz = 10.
- ii) Based on your calculation what type of a G/S is it (inelastic, elastic, unit elastic)? Explain.
iii) Calculate the cross price elasticity of demand for Good Y and Good X ifIf you are told that Py = 25 and Pz = 50.
- iv) Interpret the value of the cross price elasticity of demand. What type of G/S is Good Y relative to X.
- Consider we wanted to know how many trips versus dinners out you could purchase. If you were told that X = number of trips and Y = the number of dinners out and you were given the following budget information; M=4000, Px=800, and Py=100, answer the following questions.
Note: In general we may note that W ≥Px*X + Py*Y à use M instead of W for the purposes of this question.
- Graph the budget line, and determine the market rate of substitution. Make sure to Illustrate the budget set as well as what is unaffordable. Also note the maximum amounts of both trips and dinners you can purchase given wealth/Income and prices.
- Show in your graph what happens to the budget constraint if Px decreases to $500 (i.e. the costs of trips drops).
iii. What is the meaning of the slope of the two budget constraints? Explain using the values you calculated.