Explain step by step Suppose that you own a company and that the aggregate deman

Question

Explain step by step

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 I is income. Further suppose that the price of your product (P) is $100, the prices of related goods (P_1 and P_2) are $20 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 normative) 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

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

Plugging in the values,

QD = 8,000 - 100 + (10 x 20) - (50 x 30) + (0.02 x 100,000) = 8,000 - 100 + 200 - 1,500 + 2,000 = 8,600

(a) Cross-price elasticity = (dQD / dP2) x (P2 / QD)

= - 50 x (30 / 8,600) = - 0.17

(b) This cross price elasticity indicates that, as price of related good 2 increases (decreases) by 1%, quantity demand of the good in question will decrease (increase) by 0.17%.

(c) Since absolute value of cross elasticity of demand with good 2 is less than 1, the relationship is inelastic.

(d) Since cross price elasticity of demand with related good 2 is negative, my product and good 2 are complements: The rise (fall) in price of good 2 causes a fall (rise) in quantity demanded of my product since these two are consumed together.

Note: First 4 sub-parts are answered.

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