# Demand Estimation

**Topics:**Supply and demand, Marginal cost, Demand curve

**Pages:**24 (5612 words)

**Published:**May 7, 2013

1a)

The demand curve for haircuts at Terry Bernard’s Hair Design is P = 15 – 0.15Q where Q is the number of cuts per week and P is the price of a haircut. Terry is considering raising her price above the current price of RM9. Terry is unwilling to raise price of the price hike will cause revenue to fall. Should Terry raise the price of haircuts above RM9? Why or why not?

b)

Terry is trying to decide on the number of people to employ based on the following short-run production function:

Q = 12L – 0.5L2

Where Q is the number of cuts per week and L is the number of workers. Suppose the price of a haircut is RM9, how many people should be hired if she pays each worker RM60 per week.

2. Based on a consulting economist report, the demand function for Formula 1 stickers by two individuals, (assuming the market has only 2 individuals)

Q1 = 16 - 4PQ2 = 20 –2P respectively

a. What is the market demand curve equation? Write it in the conventional way. b. Given the total cost as TC = 2 + 0.9Q2. Calculate the profit maximizing quantity and price and the total profits. c. Draw a diagram showing the equilibrium situation in (b).

3. The market demand and supply functions for a consumer item are as follow:

Qd = 120 – 6P

Qs = 20 +4P

a) Determine the equilibrium price and quantity.

b) If the government sets a minimum price of $12 per unit, how many units would be supplied and how many units would be demanded? c) If demand increases to : Qd’ = 200 – 6P, determine the new equilibrium price and quantity. d) Draw a figure showing equilibrium price and quantity as in part (a) and part (c).

4. Zaid’s Frozen Pizza have enjoyed rapid growth in West Malaysia. From the analysis, it was found that the demand curve follows this pattern

Q = 1,000 – 3,000P + 10A

Where,

Q = Quantity demanded

P = Product Price (in RM)

A = Advertising expenditure (in RM)

a. Assume that P = 3 and A = 2,000. Suppose the firm reduces price. Would this increase total revenue? Explain. b. Assume that P = 4 and A = 2,100. Suppose the firm reduces price. Would this increase total revenue? Explain.

5. Given the following supply and demand equations

Qd = 102 – 6P

Qs = 11 + 6P

a. Determine the equilibrium price and quantity.

b. If the government sets a minimum price of $9 per unit, how many units would be supplied and how many would be demanded? c. If the government sets a maximum price of $5 per unit, how many units would be supplied and how many would be demanded? d. If demand increases to Q’d = 200 – 5P, determine the new equilibrium price and quantity.

6. The Rosenburg Corporation, a maker of machine tools, determines that the demand curve for its products is as follows:

P = 1,000 – 40Q

Where P is the price (in dollars) of a machine tool, and Q is the number of machine tools sold per month.

a. What is the price elasticity of demand if price equals $500? b. At what price, if any, will demand for Rosenburg’s product be of unitary elasticity? c. Using the above equation, determine the output rate that maximizes total revenue of Rosenburg’s Corporation? d. Illustrate your answer using TR, AR and MR functions showing various degrees of elasticities.

7. David & Sons Co. Ltd producing standard steel bars has following demand curve:

P = 2000 – 20Q

Where P is the price, and Q is the number sold per month.

a. Derive the marginal revenue curve for the firm.

b. At what output is the demand for the firm’s product price elastic? c. If the firm wants to maximize its dollar sales volume, what price should it charge?

8. Eye-de-ho Potatoes is a product of the Coeur d’ Alene Growers’ Association. Producers in the...

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