A consumer's preferences over two goods (x1, x2) are represented by the utility function u(x1,x2) =...

 

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A consumer's preferences over two goods (x1, x2) are represented by the utility function u(x1,x2) = 5x + 2x2. The income he allocates for the consumption of these two goods is m. The prices of the two goods are p and p2, respectively. < (i) Determine the monotonicity and convexity of these preferences and briefly define what they mean. < (ii) Interpret the marginal rate of substitution (MRS(x1, x2)) between the two goods for this consumer. W (iii) For any P1, P2, and m, calculate the Marshallian demand functions of x and x2 including the corner solutions if they exist. < (iv) Consider a price change in x from p = 10 to p = 20 assuming p2 = 5 and m = 50. Calculate the substitution effect (SE) and income effect (IE) on x for the given price change. Considering this range of price change only, are these goods normal or inferior? Are they ordinary or Giffen? Explain using the SE and IE that you calculated. < (v) Is x normal or inferior in general? Is it ordinary or Giffen in general? Briefly explain. Make sure to include its behaviour at the corner solutions (if they exist). A consumer's preferences over two goods (x1, x2) are represented by the utility function u(x1,x2) = 5x + 2x2. The income he allocates for the consumption of these two goods is m. The prices of the two goods are p and p2, respectively. < (i) Determine the monotonicity and convexity of these preferences and briefly define what they mean. < (ii) Interpret the marginal rate of substitution (MRS(x1, x2)) between the two goods for this consumer. W (iii) For any P1, P2, and m, calculate the Marshallian demand functions of x and x2 including the corner solutions if they exist. < (iv) Consider a price change in x from p = 10 to p = 20 assuming p2 = 5 and m = 50. Calculate the substitution effect (SE) and income effect (IE) on x for the given price change. Considering this range of price change only, are these goods normal or inferior? Are they ordinary or Giffen? Explain using the SE and IE that you calculated. < (v) Is x normal or inferior in general? Is it ordinary or Giffen in general? Briefly explain. Make sure to include its behaviour at the corner solutions (if they exist).