Question #1: Solving for Income and Substitution Effects Fernando loves to garden and purchases garden gnomes (G) and garden hoes (H). Fernando has the following utility function, U(G,H) = G4 H3/4. Suppose that Fernando has an income of $830 and the initial price of a garden gnome (PG) is equal to $15 and the price of a garden hoe (PH) is equal to $10. (a) Use the Lagrangian Method to solve for the optimal basket of goods. (b) Calculate the utility that Fernando receives if he consumes the optimal basket. (c) Suppose that the price of garden gnomes rises to $25 per unit. Use the Lagrangian Method to solve for the new optimal basket of goods. Find the total effect of the price change on the consumption of each good. (d) Find the substitution effect of the increase in the price of garden gnomes on the consumption of each good. (e) Find the income effect of the decrease in the price of garden gnomes on the consumption of each good. Are the goods normal or inferior? Briefly explain your answer.
Question #1: Solving for Income and Substitution Effects Fernando loves to garden and purchases garden gnomes (G) and garden hoes (H). Fernando has the following utility function, U(G,H) = G4 H3/4. Suppose that Fernando has an income of $830 and the initial price of a garden gnome (PG) is equal to $15 and the price of a garden hoe (PH) is equal to $10. (a) Use the Lagrangian Method to solve for the optimal basket of goods. (b) Calculate the utility that Fernando receives if he consumes the optimal basket. (c) Suppose that the price of garden gnomes rises to $25 per unit. Use the Lagrangian Method to solve for the new optimal basket of goods. Find the total effect of the price change on the consumption of each good. (d) Find the substitution effect of the increase in the price of garden gnomes on the consumption of each good. (e) Find the income effect of the decrease in the price of garden gnomes on the consumption of each good. Are the goods normal or inferior? Briefly explain your answer.
Chapter21: Demand: Consumer Choic
Section: Chapter Questions
Problem 1E
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Transcribed Image Text:Question #1: Solving for Income and Substitution Effects
Fernando loves to garden and purchases garden gnomes (G) and garden hoes (H). Fernando has the
following utility function, U(G,H) = G4 H3/4. Suppose that Fernando has an income of $830 and
the initial price of a garden gnome (PG) is equal to $15 and the price of a garden hoe (PH) is equal to
$10.
(a) Use the Lagrangian Method to solve for the optimal basket of goods.
(b) Calculate the utility that Fernando receives if he consumes the optimal basket.
(c) Suppose that the price of garden gnomes rises to $25 per unit. Use the Lagrangian Method to solve
for the new optimal basket of goods. Find the total effect of the price change on the consumption of each
good.
(d) Find the substitution effect of the increase in the price of garden gnomes on the consumption of each
good.
(e) Find the income effect of the decrease in the price of garden gnomes on the consumption of each
good. Are the goods normal or inferior? Briefly explain your answer.
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