Suppose that you own a company and that the aggregate demand for your product ca

Question

Suppose that you own a company and that the aggregate demand for your product can be written as: Q^D= 8,000-P + 10P_1 - 50P_2 + 0.02I where P is the price of your product, P_1 and P_2 are prices of related goods (which we will refer to as related goods 1 and 2), and/is income. Further suppose that the price of your product (P) is $100, the prices of related goods (P_1 and P_1) are S20 and S30 respectively, and income is $100,000. What is the cross-price elasticity for related good 2? Show your work and round your calculation to two decimal places if necessary. Describe what the magnitude of your answer to means verbally, (i.e. What positive (as opposed to nonnative) economic relationship is the value that you calculated telling you? Be precise.) Indicate whether the relationship in is inelastic, elastic, or unit elastic. Explain why. Are your product and related good 2 substitutes or complements? Explain your answer using an argument based on microeconomic theory. What is the equation for the inverse demand curve at the current prices of goods 1 and 2 and current income? What is the "choke" price for this demand curve?

Explanation / Answer

Answer:

The aggregate demand of the company is:

      QD = 8,000 – P + 10P1 – 50P2 + 0.02I

Where: P = $100

                P1 = $20

                P2 = $30

                I = $100,000

Now, we can substitute the above all values in to the demand function, then we get the aggregate demand is:

      QD = 8,000 – 100 + 10(20) – 50(30) + 0.02(100,000)

      QD = $8,600

What is the cross-price elasticity for related good2?

    The cross-price elasticity of demand (EC) is equals to percentage change in X quantity is divided by the percentage change in Y price. That is:

                EC = (%Q of X)/(%P of Y)

Here the product (P) is $100 and the related good2’s price (P2) is: $30, and

The related good1’s quantity is 200, i.e., 10 * 20 = 200.

Now, the cross-price elasticity for related good2 is:

                EC = {[200 + 100/(200 -100)/2]/[20 + 100/(20 – 100)/2)]}

                EC = (300/50)/(120/-80)

                EC = -120/60

                EC = -2

Indicate whether the relationship in part-a is inelastic, elastic, or unit elastic?

We know, If Elasticity < 1 (absolute value) = Inelastic

If Elasticity > 1 (absolute value) = Elastic

If Elasticity = 1 (absolute value) = Unit Elasticity

Here -2 < 1 therefore, the relation is: Inelastic

Are your product and related good2 substitute or complements?

    We know, if elasticity of good x and good y (Exy) > 0, it is substitute goods, if elasticity of good x and good y (Exy) < 0, it is complementary goods and if elasticity of good x and good y (Exy) = 0, it is unrelated goods. Here related good2 elasticity is: -2. Therefore, it is the complementary good.

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