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Question #1: Solving for Income and Substitution Effects Gillian loves to garden and purchases garden gnomes (G) and garden hoes (H). Gillian has the following utility function, U(G,H) = GmH. Suppose that Gillian has an income of $1035 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 Gillian receives if she consumes the optimal basket. (c) Suppose that the price of garden gnomes falls to $5 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 decrease in the price of garden hoes on the consumption of each good. (e) Find the income effect of the decrease in the price of garden hoes on the consumption of each good. Are the goods normal or inferior? Briey explain your answer. (f) Draw a graph with G on the Y-axis and H on the X-axis that depicts the Total Effect and its decomposition into the Substitution Effect and Income Effect