Convexity & Concavity Consider the function defined by the formula This function is 200 if 0 < x < 20 x y = f(x) = 30- x if 20 ≤x≤40 200 if 40 < x < 60 x a. Concave but not strictly concave b. Strictly convex c. Strictly concave d. Convex but not strictly convex e. I cannot tell because the second derivative of f(x) cannot be calculated

2. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility.

Consider the relationship y = f(x). In this relationship: %3D Oa. y is called the independent variable and x is called the dependent variable. O b. y is called the range and x is called the domain. O c. yis called the dependent variable and x is called the independent variable. O d. y is called the domain and x is called the range.

Graphical and Intuitive Optimization Consider a consumer who must allocate their available income between the consumption of two goods, Beer and Pizza.  Their preferences over Beer and Pizza adhere to the usual assumptions we have made about preferences. The indifference curve map below reflects their preferences and the budget constraint reflects current income and prices. In the simplest terms possible, define or explain the term "Marginal Utility of Beer" (MUB). In the simplest terms possible, define or explain the term "Marginal Rate of Substitution of beer for pizza" (MRSBP). In the simplest terms possible, intuitively explain the meaning of MUB/PB, where PB represents the price of one unit of Beer.

The value in Y axis has changed from 13.54 to 11.78 and the value in X axis has changed from 9.96 to 4.14, what is the slope of the indifference curve at this point?     a. 0.30 b. -3.31 c. -8.01 d. 11.22

A consumer buys only two goods, X and Y. No other goods exist and there is no possibility of saving. The marginal utility of X is independent of the quantity of Y consumed, and the marginal utility of Y is independent of the quantity of X consumed. MUX is constant no matter how he consumes, but MUY falls as consumption increases. In the initial equilibrium he consumes one of each good. How much can you infer about the following: a.) The slope of the indifference curve b.) The curvature of the indifference curve c.) Whether the marginal utility of money is constant, rising, or falling as money income increases. d.) the income elasticity of demand for Y e.) The price elasticity of demand for X.

The Law of Demand states that as the price of a good increases, ceteris penbus, the The relationship that exists between these two variables can be described as decreases. This can be shown graphically with demand curve or numericaly in a table using a 0

. On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according to thefunctionU (c, b) = 20c - c2 +18b- 3b2.How many cigars and glasses of brandy does he consume during an evening? (Cost is no objectto J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum of glasses ofbrandy and cigars consumed to 5. How many glasses of brandy and cigars will he consumeunder these circumstances?

80 60 40 20 0 a N b A 10 a Multiple Choice 20 B 30 C 40 b C NE 50 60 Refer to the diagram. The slope of curve ZZ at point A is approximately

Jane insists on consuming 4 bowls of yogurt with 2 bananas. If the price of banana is $1 per unit and the price of yogurt is $1 per bowl, then if Jane income is $m, the slope of the Engel curve for bananas will be (a) negatíve and constant. (b) negative and increasing. (c) zero. (d) positive and constant. (e) None of the above.