b) find the price in dollars per pund that will maximize the revenue. **Columbia's Coffee Export Demand Analysis**Columbia, a South American country, exports coffee and estimates that the demand function is given by:\[ D(p) = 63 - 2p^2 \]**Question:**a) If the country wants to raise revenues and improve its balance of payments, should it raise or lower the price from the present level of $3 per pound?**Hint:** You may need to use the formula for the elasticity of demand:\[ E(p) = -\frac{p \cdot D'(p)}{D(p)} \] **Explanation:**- **Demand Function:** This function shows how the price of coffee affects the quantity demanded. The equation $ D(p) = 63 - 2p^2 $ indicates that as the price $ p $ increases, the demand $ D(p) $ decreases.- **Elasticity of Demand:** The elasticity of demand measures how sensitive the quantity demanded is to a change in price. The negative sign in $ E(p) = -\frac{p \cdot D'(p)}{D(p)} $ indicates the inverse relationship between price and demand.To determine whether to raise or lower the price, one would need to calculate the elasticity at $ p = 3 $ and analyze whether the demand is elastic, inelastic, or unitary elastic at that price level. If demand is elastic (elasticity greater than 1), lowering the price could increase total revenue. If demand is inelastic (elasticity less than 1), raising the price could lead to higher revenue.

Given: Q = 63 - 2p2 If price is $3 Q= 63 - 2*9 Q = 45 unitsNow, as the demand is inelastic this means a rise in price will cause a lesser fall in quantity. Thus, price should be raised in order to increase revenue.Q = 63 - 2p2 TR = p*Q TR = 63p-2p3 To maximize TR, we will differentiate it and equate it will zero: dTR/dp = 63-6p2 =0 p2 = 10.5 p=$3.24 Thus, the price should increase to $3.24 in order to maximize TR.

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Columbia, a South American country, exports coffee and estimates that the demand function to be D(p) = 63 – 2p². a) If the country wants to raise revenues to improve its balance of payments, should it raise or lower the price from the present level of $3 per pound? p-D'(p) D(p) Hint: You may need to use the formula for the elasticity of demand, E (p) : %3D

Columbia, a South American country, exports coffee and estimates that the demand function to be D(p) = 63 – 2p². a) If the country wants to raise revenues to improve its balance of payments, should it raise or lower the price from the present level of $3 per pound? p-D'(p) D(p) Hint: You may need to use the formula for the elasticity of demand, E (p) : %3D

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

b) find the price in dollars per pund that will maximize the revenue.

**Columbia's Coffee Export Demand Analysis**

Columbia, a South American country, exports coffee and estimates that the demand function is given by:

\[ D(p) = 63 - 2p^2 \]

**Question:**

a) If the country wants to raise revenues and improve its balance of payments, should it raise or lower the price from the present level of $3 per pound?

**Hint:** You may need to use the formula for the elasticity of demand:

\[ E(p) = -\frac{p \cdot D'(p)}{D(p)} \]

**Explanation:**

- **Demand Function:** This function shows how the price of coffee affects the quantity demanded. The equation $ D(p) = 63 - 2p^2 $ indicates that as the price $ p $ increases, the demand $ D(p) $ decreases.

- **Elasticity of Demand:** The elasticity of demand measures how sensitive the quantity demanded is to a change in price. The negative sign in $ E(p) = -\frac{p \cdot D'(p)}{D(p)} $ indicates the inverse relationship between price and demand.

To determine whether to raise or lower the price, one would need to calculate the elasticity at $ p = 3 $ and analyze whether the demand is elastic, inelastic, or unitary elastic at that price level. If demand is elastic (elasticity greater than 1), lowering the price could increase total revenue. If demand is inelastic (elasticity less than 1), raising the price could lead to higher revenue.

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