Economists working for a computer-manufacturing corporation conclude that the demand function for the corporation’s brand of...

Economists working for a computer-manufacturing corporation conclude that the demand function for the corporation’s brand of laptop is

Q = - 700P + 200M – 500S + 0.01A

Where Q equals the quantity of laptops demanded, P is the price of the laptop, M is the per capita disposable income per year, S is the average price of software, and A is the amount the company spends on advertising.

At present P = $3,000, M = $13,000, S = $400, and A = 50 million

a. What is the price elasticity of demand for the corporation’s laptop? Is demand elastic, inelastic, unit elastic? What does your result say about the sensitivity of quantity of laptops demanded to price changes?

b. The CEO of the corporation wants to know if the company is maximizing it sales revenue by charging $3000 for its laptop. Is the corporation maximizing it sales revenue? If yes, why? If not, what price should it charge to maximize its revenue?

c. What is the cross-price elasticity of demand between the quantity of laptops demanded and the price of the software? Explain how a 5% decrease in price of the software (S) would affect the demand for the laptop.

d. What is the income elasticity of demand of the laptop? Economists foresee an economic boom for next year. How would a 4% increase in per capita disposable income affect the demand for the laptop?

e. What is the advertising elasticity of demand? If the corporation wants to increase its sales by 5% by changing its ad expenditures, what should it do? Increase or decrease its ad expenditures? By what percentage amount?

Expert Solution

,
Q = - 700P + 200M – 500S + 0.01A

Plugging the values, P= $3,000, M = $13,000, S = $400, and A = 50 million, we get Q= 800,000.

Pro tip: Please use the formula for elasticity as (dQ/Q)/(dP/P) = (dQ/dP)* (P/Q), wherever possible. This gives precise value of point elasticity. If you use the concept of changes in price, i.e. delta, you might have to take the averages of both Q's and both P's.

(a) At this point, PED= %change in Demand of Q/ % change in price of Q, which gives, PED= (dQ/Q)/(dP/P) = (dQ/dP)* (P/Q), which comes out as -2.63. Hence, the demand is elastic, and sensitive to changes in price

(b) For profit maximising Revenue, TR= TC and MR= MC, I need info on marginal cost for the product (Please provide the same in comments below).

(c) Currently S= 400, if decreased by 5%, it becomes 380, and Q= 810,000
Cross Price elasticity of Demand, CPE= (dQ/Q)/(dP (software/ P (software)) = (dQ/dS) * (S/Q). which gives CPE=0.19 Hence, the demand is inelastic, and not sensitive to changes in price of software.

(d) Currently M= 13000, if increased by 4%, it becomes 13520, and Q= 904,000
IED= (dQ/Q)/(dM/M), hence, dQ/dM)* (Q/M) = (dQ/dM) * (M/Q)= 2.99. Hence, the demand is elastic, and sensitive to changes in income. Please note that elasticity is positive here, i.e. increasing income leads to increasing quantity!

(e) Advertising elasticity of demand. A = 50 million and Q= 800000. If Q is to be increased to 840,000 (i.e. by 5%), A must be equal to 54 million (plug in values of Q and all other values, to get new value of A). Hence, we need to increase A by 8% for an increase in Q of 5%. Hence, the demand is inelastic.
We can use the conecpt of elasticity too, i.e. AED= dQ/dA)* (Q/A) = (dQ/dA) * (A/Q) = 0.01* (54,000,000/ 840,000) = 0.64. Hence, the demand is inelastic, and not sensitive to changes in Advertisement.

Long question this, please let me know if any calculations are incorrect. Please provide marginal cost values for (b)

Rahul Sunny answered 2 years ago

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