Question 1: What is the derivative of f(x) = 3x²?
6x 3x 9x² 3/2x
Question 2: For the utility function U(x₁, x₂) = x₁ + x₂, what is the Marginal Rate of Substitution (MRS)?
x₂/x₁ 1 x₁x₂ 0
Question 3: If a consumer has income m = 100 and faces prices p₁ = 2 and p₂ = 5, what is the x-intercept of their budget constraint?
20 50 25 100
Question 4: For production function \(Q = L^{0.5}K^{0.5}\), what type of returns to scale does the firm exhibit?
Increasing Decreasing Constant Cannot be determined
Question 5: For utility function \(U(x_1, x_2) = x_1^{0.3} x_2^{0.7}\), what proportion of income will the consumer spend on good 1?
0.7 0.3 1.0 Cannot be determined without prices
Question 6: If C(q) = q² + 4q + 16, what is the Average Variable Cost (AVC)?
q + 4 q + 4 + 16/q 2q + 4 q² + 4q
Question 7: For production function \(Q = 4L^{0.5}\), if the wage is w = 8 and output price P = 2, what is the profit-maximizing quantity of labor?
1/4 1/2 4 8
Question 8: What is ∂f/∂x₁ for f(x₁, x₂) = 3x₁²x₂?
6x₁x₂ 3x₁² 3x₂ 6x₁
Question 9: A firm with production function \(Q = L^{0.75}K^{0.25}\) faces factor prices w = 16 and r = 4. What is the cost-minimizing ratio of L to K?
1:1 3:4 4:1 3:1
Question 10: For cost function C(q) = q³ - 8q² + 30q + 50, at what quantity does Average Variable Cost reach its minimum?
4 8 10 16
Question 11: Consider a consumer with the following choices:
Do these choices violate WARP?
Yes, because both bundles are affordable at both price vectors No, because bundle A is not affordable when B is chosen Yes, but only if we assume local non-satiation
Question 12: For production function \(Q = x_1^{0.4}x_2^{0.8}\), by what factor does output increase when all inputs are doubled?
1.2 2 \(2^{1.2}\) \(2^{2.4}\)