ll T-Mobile Wi-Fi 9:16 PM 2018 ASSIGNMENT 3.pdf 12018/ Dr. FERNANDEZ ASSIGNMENT

Question

ll T-Mobile Wi-Fi 9:16 PM 2018 ASSIGNMENT 3.pdf 12018/ Dr. FERNANDEZ ASSIGNMENT 3 DUE MONDAY, JULY 16 BY 11:59PM 1 The general linear demand for good X is estimated to be - 18,000- 175P 0.35M 16P where P is the price of good X M is average income of consumers who buy good X and Pr is the price of related good R·The values of f·M, and Pa are expected to be $65. S52.000, and $100. respectively. Use these values at this point on demand to make the following computations a. Compute the quantity of good Xdemanded sor the given values of P. M and P Calculate the price elasticity of demand E. At this point on the demand for X is demand elastic, inelastic, or unitary elastic? How would increasing the price of Xaffect total revenue? Explain. e. Calculate the income elasticity of demand Eu Is good X normal or inferioer? Explain howa 1.75 percent decrease in income would affect demand for X all other factors affecting the demand for X remaining the same. d Calculate the cross-price elasticity Eux Are the goods X and R substitutes or complements? Explain how a 2.5 percent increase in the price of related good R would affect demand for X all other factors affecting the demand for Xremaining the same. 21Smer 201 Open With Print

Explanation / Answer

a).

Consider the demand curve for “X” as follows.

=> Q = 18,000 – 175*P + 0.35*M – 16*Pr, where “P=65”, “M=52,000” and “Pr=1,00”. So, the quantity demanded at the given values of “P”, “M” and “Pr” is given below.

=> Q = 18,000 – 175*65 + 0.35*52,000 – 16*1,00 = 23,225, => Q = 23,225. So, here the total output demanded is “Q=23,225”.

b).

The demand for “X” is given by, “Q = 18,000 – 175*P + 0.35*M – 16*Pr”, => dQ/dP = (-175).

=> the price elasticity is given by, E = (dQ/dP)*(P/Q) = (-175)*(65/23,225) = (-0.4898)=(-0.49).

So, here the elasticity is “-0.49”, => the absolute value of the elasticity is “0.49” which is less than “1”, => here the demand is relatively inelastic.

So, as the demand is relatively inelastic, => as “P” increases implied “total revenue” also increases. So, there is a direct relational ship between them.

C).

Now, according to the demand curve, “dQ/dM = (0.35)”, => the income elasticity is given by.

=> Em = (dQ/dM)*(M/Q) = (0.35)*(52,000/23,225) = 0.78 < 1.

So, as the income elasticity is positive, => the good is a normal good.

So, here the income elasticity of demand is “0.78”, => if “income” increases by “1%” implied the quantity demanded also increases by “0.78%”. So, here if “income” decreases by “1.75%”, => the quantity demanded decreases by “1.75*0.78 = 1.37%”.

d).

Now, given the demand curve “dQ/dPr = (-16)”, => the cross price elasticity of demand is given by, “Ep = dQ/dPr*(Pr/Q) = (-16)*100/23,225 = (-0.07) < 0”.

So, here the cross price elasticity is negative, => here the good is complement to “X”, => as “Pr” increases the quantity demanded decreases and vice versa.

Now, here the cross price elasticity is “-0.07”, => as “Pr” increases by “1%”, => the quantity demanded for “X” decreases by “0.07%”. So, here if “Pr” increases by “2.5%”, => the quantity demanded for “X” decreases by “0.07*2.5=0.18%”.

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