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Cash flow . What is the appropriate discount rate to apply to the target’s cash flows?. Discounting the target’s cash flows. The cash flows reflect the target’s business risk, not the acquiring. However, the merger will affect the target’s leverage and tax rate, hence its financial risk.. The target firm has 10 million shares. The acquirer estimates the maximum price...
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All explanations of mathematical concepts are set out in the context of applications in economics.. continuous growth. Improved pedagogical features, such as learning objectives and end of chapter ques- tions, along with an overall example-led format and the use of Microsoft Excel for relevant applications mean that this textbook will continue to be a popular choice for both students and...
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It does not just describe what goes on in the economy. An economist also needs to be able to say by how much price is expected to rise if supply contracts by a specified amount. For example, the relationship between the quantity of apples consumers wish to buy and the price of apples might be expressed as: ‘the quantity of...
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Most students will have previously covered all, or nearly all, of the topics in this chapter.. Only a fairly brief explanation is given for most of the arithmetical rules set out in this chapter. However, apart from simple addition and subtraction problems, it is usually quicker to use a pocket calculator for basic arithmetical operations. Test Yourself, Exercise 2.1 1....
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The total cost of the amount of flour the firm uses will therefore be 0.2q times a , written as 0.2qa.. For example, an expression for the length of fencing (in metres) needed to enclose a square plot of land of as yet unknown size can be constructed as follows:. Once the value of A is specified then we can...
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A relationship between the values of two or more variables can be defined as a function when a unique value of one of the variables is determined by the value of the other variable or variables.. If the precise mathematical form of the relationship is not actually known then a function may be written in what is called a general...
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the demand schedule and the supply schedule then the equilibrium values of p and q will be such that both equations (1) and (2) hold. Find the equilibrium values of p and q.. (a) Find the equilibrium values of p and q.. What combination of A and B that uses up all the budget is it possible to purchase at...
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Use the quadratic equation solution formula.. A quadratic equation is one that can be written in the form ax 2 + bx + c = 0. A quadratic equation that includes terms in both x and x 2 cannot be rearranged to get a single term in x, so we cannot use the method used to solve linear equations.. There...
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Calculate the final sum, the initial sum, the time period and the interest rate for an investment.. F is the final value of the investment,. i is the interest rate per time period (as a decimal fraction) and n is the number of time periods.. The formula for the final value F of an investment of £A for n time...
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Find the slope of a function using differentiation.. Derive marginal revenue and marginal cost functions using differentiation and relate them to the slopes of the corresponding total revenue and cost functions.. This chapter introduces some of the basic techniques of calculus and their application to economic problems. Differentiation is a method used to find the slope of a function at...
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Find the maximum or minimum point of a single variable function by differenti- ation and checking first-order and second-order conditions.. ‘when is TR at its maximum?’ the answer is obviously at M, which is the highest point on the curve. At M itself the slope is zero.. Zero slope will not guarantee that a function is at a maximum, as...
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10.1 Partial differentiation and the marginal product. For the production function Q = f(K, L) with the two independent variables L and K the value of the function will change if one independent variable is increased whilst the other is held constant. For any given value of L this is the slope of the TP L function. For example, the...
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11.1 Constrained optimization and resource allocation. 11.2 Constrained optimization by substitution. A firm faces the production function Q = 12K 0.4 L 0.4 and can buy the inputs K and L at prices per unit of £40 and £5 respectively. Substituting (2) into the objective function Q = 12K 0.4 L 0.4 gives. A firm faces the production function Q...
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Check the second-order conditions for optimization of relevant economic func- tions using the quotient rule for differentiation.. 12.1 Overview. These are the chain rule, the product rule and the quotient rule. 12.2 The chain rule. Assume, for example, that you wish to find an expression for the slope of the non-linear demand function. dq = −0.2 dp. Thus, using the...
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13.1 Dynamic economic analysis. 13.2 The cobweb: iterative solutions. The cobweb model takes into account this delayed response on the supply side of a market by assuming that quantity supplied now (Q s t ) depends on the ruling price in the previous time period (P t − 1. where the subscripts denote the time period. In the cobweb model...
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14.1 Continuous growth and the exponential function. You will recall that the final value (F ) of an initial investment (A) deposited for t discrete time periods at an interest rate of i can be calculated from the formula. When the nominal annual rate of interest is 100% (i = 1) and the initial sum invested is assumed to be...
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The addition, or subtraction, is performed on each of the corresponding elements.. Total sales for each week will simply be the sum of the corresponding elements in matrices A and B. If one matrix is multiplied by another matrix, the basic rule is to multiply elements along the rows of the first matrix by the corresponding elements down the columns...
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11.641754 6. 25.000655. 0.5w + 0.25 6. Own example 7. 10.5x + 6y 8. Own example. Own example 3.7 1. 13.25%, 8.2. Own example 4.3 (Answers to 1 to 5 give intercepts on axes). Own example 4.7 1. Own example 3. (a) 3,125L − 1.25 (b) 9.882 (c) increasing. (a) 4,093.062L − 1.7714 (b) 1.173 (c) decreasing 4.11 1. Own...
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Econometric Analysis of Cross Section and Panel Data. 1.1 Causal Relationships and Ceteris Paribus Analysis 3 1.2 The Stochastic Setting and Asymptotic Analysis 4. 2 Conditional Expectations and Related Concepts in Econometrics 13 2.1 The Role of Conditional Expectations in Econometrics 13. 2.2.2 Partial E¤ects, Elasticities, and Semielasticities 15 2.2.3 The Error Form of Models of Conditional Expectations 18 2.2.4...
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In this part we introduce the basic approach to econometrics taken throughout the book and cover some background material that is important to master before reading the remainder of the text. Students who have a solid understanding of the algebra of conditional expectations, conditional variances, and linear projections could skip Chapter 2, referring to it only as needed. Chapter 3...