The extended demand function of good Y is: Q d Y = 140 – 2 P Y - 1 P X - .01 M c

Question

The extended demand function of good Y is:

QdY = 140 – 2 PY - 1 PX - .01 M

c)

If M = 1,000, PX = 5, and if PY = 10 then QdY = ________

If M = 1,000, PX = 5, and if PY = 15 then QdY = ________

Use these two prices and quantities demanded to calculate the value of the price elasticity of demand between these two points on the demand curve for good Y (use the arc elasticity formula). Show your work and interpret your answer using a 10% change in price. What will happen to revenues for the suppliers of good Y as the price of good Y increases within PY = 10 and PY = 15? WHY?

d) You found that when:

M = 1,000, PX = 5, and PY = 10 then QdY = ________

Now let’s suppose that the average consumer income increases from 1,000 to 2,000 but the price of good X remains constant at 5 and the price of good Y remains constant at 10. In other words, if

M = 2,000, PX = 5, and PY = 10 then QdY = ________

Use these two average consumer income levels and associated quantities demanded of good Y to calculate the value of the income elasticity of the demand for good Y (when PX = 5 and PY = 10). Show your work and interpret your answer using a 10% change in income. Based on the value of the income elasticity of demand you just estimated, what type of good is good Y? WHY?

e) You found that when:

M = 1,000, PX = 5, and PY = 10 then QdY = ________

Now let’s suppose that the price of good X increases from 5 to 8 (but income remains constant at 1,000 and the price of good Y remains constant at 10). In other words, if

M = 1,000, PX = 8, and PY = 10 then QdY = ________

Use these prices of good X and the quantities demanded of good Y to calculate the cross-price elasticity of the demand of good Y when the price of good X increases from 5 to 8 (and PY =10 and M = 1,000). Show your work and interpret your answer using a 10% change in the price of good X. Based on the value of this cross-price elasticity of demand you just estimated, what type of goods are Y and X? WHY?

Explanation / Answer

(c) QdY = 140 – 2 PY - 1 PX - .01 M

(i)

M = 1,000, PX = 5, and if PY = 10 then QdY = 140 - (2 x 10) - (1 x 5) - (0.01 x 1,000)

= 140 - 20 - 5 - 10 = 5

If M = 1,000, PX = 5, and if PY = 15 then QdY = 140 - (2 x 15) - (1 x 5) - (0.01 x 1,000)

= 140 - 30 - 5 - 10 = - 5

(iii) Arc Price elasticity of demand, eP = [(Q2 - Q1) / (Q2 + Q1) / 2] / [(P2 - P1) / (P2 + P1) / 2]

= [(-5 - 5) / 0] / [(P2 - P1) / (P2 + P1) / 2]

Since division by 0 is meaningless, in this case we cannot compute eP using the Arc elasticity formula.

(iv) Cannot be computed, since Arc elasticity cannot be calculated.

(d) QdY = 140 – 2 PY - 1 PX - 0.01 M

M = 1,000, PX = 5, and PY = 10 then QdY = 140 - (2 x 10) - (1 x 5) - (0.01 x 1,000)

= 140 - 20 - 5 - 10 = 5

M = 2,000, PX = 5, and PY = 10 then QdY = 140 - (2 x 10) - (1 x 5) - (0.01 x 2,000)

= 140 - 20 - 5 - 20 = - 5

As in case (a) above, elasticity of income cannot be calculated using the method of averages because it will mean a division by 0 which is mathematical impossibility.

So, next part of question also cannot be computed.

(e) QdY = 140 – 2 PY - 1 PX - 0.01 M

M = 1,000, PX = 5, and PY = 10 then QdY = 5 (As calculated in above parts)

M = 1,000, PX = 8, and PY = 10 then QdY = 140 - (2 x 10) - (1 x 8) - (0.01 x 1,000)

= 140 - 20 - 8 - 10 = 2

Cross price elasticity = Change in QdY / Change in Px

= [(2 - 5) / 5] / [(8 - 5) / 5]

= - 0.60 / 0.60

= - 1

This means that, as Price of X increases (decreases) by 1%, quantity demanded of Y decreases (increases) by 1%.

Therefore, as Price of X increases (decreases) by 10%, quantity demanded of Y decreases (increases) by 10%.

Since cross-price elasticity is negative, X & Y are complements.

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