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# Problems using price and income elasticity

FIRST QUESTION
Assuming the price elasticity of a companyĆ¢??s product is between -0.3 and -0.4 and the income elasticity of demand is 0.5:
1. Determine the effects a 15% price increase would have on the demand for the product
2. Determine the effect a 50% increase in income would have on the demand for the product

SECOND QUESTION
Assuming Q=At ?K ? with Q being the output rate, t being labor input rate, K being the capital input rate, alpha being 0.8 and beta being 0.3:
1. Determine if the company has increasing or decreasing returns on scale.
2. Determine if the company has increasing or decreasing returns on scale if beta is changed to 0.2.
3. Explain whether or not the per unit output of labor depends solely on alpha and beta.

THIRD QUESTION
A company made and sold 10,000 bikes last year. When output was between 5K and 10K bikes, the VC was \$24. In the output range, each bike contributed 60% of its revenue to FC and profits.
1. What is the price of the bike
2. If the company raises prices by 10%, how many bikes will need to be sold to obtain the same amount of profit as last year
3. If the company raises prices by 10%, and VC increases by 8%, how many bikes will need to be sold to obtain the same amount of profit as last year

FOURTH QUESTION

Assume the following:
Market Bundle/ Corn consumption (Vertical axis) / Peas consumption (horizontal axis)

1/2/8
2/3/7
3/4/6
4/5/5
5/6/4
6/7/3
7/8/2
8/9/1

1. Draw the indifference curve that includes the above market bundles.
2. Determine a) the MR of substitution of peas for corn, b) how this MR of substitution varies as more corn and less peas are consumed and c) if the change is realistic.

#### Solution Preview

FIRST QUESTION
Assuming the price elasticity of a company's product is between -0.3 and -0.4 and the income elasticity of demand is 0.5:
1. Determine the effects a 15% price increase would have on the demand for the product

A price increase would not involve income elasicity, only price elasicity. For each percent increase in price, demand changes by -.3 to - .4 percent. For a 15 percent increase, demand would decline by 4.5 to 6 percent.

2. Determine the effect a 50% increase in income would have on the demand for the product

Only income elasticity is relevant here. A 50% increase in income increases demand by 25%

SECOND QUESTION
Assuming Q=At^alpha K ^beta with Q being the output rate, t being labor input rate, K being the capital input rate, alpha being 0.8 and beta being 0.3:
1. Determine if the company has increasing or decreasing returns on scale.
Increasing returns to scale occur when an increase in labor and tal inputs result in a more than proportional increase in Q. Thus we increase both t and K by some multiplier, m, and create a new production function Q'. Then we will ...

#### Solution Summary

Drawing an indifference curve; prices and profits; returns to scale.

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