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Unformatted text preview: 1/2 = 5/2 Y = 25/4 (or 6.25) from (1) from (2) (3) (4) (5) Substitute (5) into the Budget Constraint to get X: 5X + 2(25/4) = 40 5 X = 110/4 X = 110/20 X=5 12 HOMEWORK: Find the consumer equilibrium (i.e. demands for X and Y) for the following situations: 1. U(x,y) = X + Y subject to 2X + 3Y = 150 ... (HINT: draw the graph first). 2. U(x,y) = X1/3Y2/3 subject to 3X + 9Y = 3000. What can you say about your result in terms of the shares of income spent on each good? 3. U(x,y) = X + 2 Y1/2 subject to 5X + 2Y = 40. 4. Evaluate the following expressions. a) b) c) d) e) (x+y)2 (x3 + y2)2 (z y4)2 (c1/2 + b5)0 [(c1/2)8]1/2 5. Verify that the CES production function, f(K,L) = [K + L]1/, can be written equivalently as... f(K,L) = _____________ [ / K + / L]1/ Find the consumer equilibrium (i.e. demands for X and Y) for the following situations: 6. U(x,y) = 7(X1/6)3 (Y2/3)1/2 subject to 7X + Y = 800. 7. U(x,y) = [X / (X1/2)] + 6 Y1/2 subject to 3X + 2Y = 330. 13 ECON 301 LECTURE #2 Slopes A slope is the measure of steepness of a line. That is, the bigger the slope, the steeper the line. Let's consider the following linear equation of a straight line: Y = aX + b In this case the slope is determined by the coefficient "a" of the independent variable X. The vertical intercept is determined by the constant "b" and the horizontal intercept is determined by the ratio "b/a". Since we are investigating a straight line we know that the slope is constant and as such it does not matter which point on the line we evaluate the slope (we should always get the same answer). Slope = a b b/a 0 X In the special case where b = 0, we have both the vertical intercept and horizontal intercept at the origin. Slopes of Curves A tangent is a straight line that touches a curve at a single point. The line is referred to as a tangent line and the point on the curve that is touching the line is called the point of tangency. At this point of tangency, both the line and the curve will have the same val...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
 Spring '10
 sning
 Economics

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